{"id":20435,"date":"2020-01-21T10:13:38","date_gmt":"2020-01-21T04:43:38","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=20435"},"modified":"2021-07-02T15:28:13","modified_gmt":"2021-07-02T09:58:13","slug":"2nd-puc-basic-maths-question-bank-chapter-15-ex-15-3","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-basic-maths-question-bank-chapter-15-ex-15-3\/","title":{"rendered":"2nd PUC Basic Maths Question Bank Chapter 15 Circles Ex 15.3"},"content":{"rendered":"

Students can Download Basic Maths Exercise 15.3 Questions and Answers, Notes Pdf, 2nd PUC Basic Maths Question Bank with Answers<\/a> helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n

Karnataka 2nd PUC Basic Maths Question Bank Chapter 15 Circles Ex 15.3<\/h2>\n

Part – A<\/span><\/p>\n

2nd PUC Basic Maths Circles Ex 15.3 One Mark Questions and Answers<\/strong><\/p>\n

1. Show that the circle.<\/p>\n

Question 1.
\nx2<\/sup> + y2<\/sup> – 8x + 2y + 16 = 0 touches x= axis.
\nAnswer:
\nGiven g = -4, f = 1, & C = 16
\n\"2nd<\/p>\n

Question 2.
\nx2<\/sup> + y2<\/sup> – 4x + 4y + 4 = 0 touches x-axis.
\nAnswer:
\nHere g = -2, C = 4
\nHere (-2)2<\/sup> = 4 \u21d2 g2<\/sup> = C
\n\u2234 The circle touches x-axis.<\/p>\n

Question 3.
\nx2<\/sup> + y2<\/sup> + 8x + 6y + 9 = 0 touches y = axis.
\nAnswer:
\nHere f = 3 & C = 9
\n& f2<\/sup> = C \u21d2 (3)2<\/sup> = 9
\n\u21d2 Circle touches y-axis.<\/p>\n

\"KSEEB<\/p>\n

Question 4.
\nx2<\/sup> + y2<\/sup> – x + 4y + 4 = 0 touches y-axis.
\nAnswer:
\nHere f= 2 & C = 4
\n& f2<\/sup> = C \u21d2 (2)2<\/sup> = 4
\n\u21d2 Circle0 touches y-axis<\/p>\n

Question 5.
\nShow that the circle x2<\/sup> + y2<\/sup> + 4x – 3y + 4 = 0 touches x- axis.
\nAnswer:
\nHere g = 2 & C = 4
\ng2<\/sup> = C \u21d2 (2)2<\/sup> = 4
\n\u21d2 Circle touches x-axis.<\/p>\n

Question 6.
\nShow that the circle x2<\/sup> + y2<\/sup> – 3x + 8y + 16 = 0 touches y – axis.
\nAnswer:
\nHere f = 4, C = 16 & f2<\/sup> = C
\n\u21d2 (4)2<\/sup> = 16 .
\n\u2234 Circle touches y-axis.<\/p>\n

Part – B<\/span><\/p>\n

2nd PUC Basic Maths Circles Ex 15.3 Two Marks Questions and Answers<\/strong><\/p>\n

Question 1.
\nFind the length of the chord of the circle x2<\/sup> + y2<\/sup> – 6x + 4y + 5 = 0 intercepted by x-axis.
\nAnswer:
\nCentre of given circle = (3,-2), c = 5
\nLength of chord intercepted by x – axis = 2\\(\\sqrt{g^{2}-c}\\) = 2\\(\\sqrt{9-5}\\) = 2\\(\\sqrt{4}\\) = 2.2 = 4 units.<\/p>\n

Question 2.
\nFind the length of the chord of the circle x2<\/sup> + y2<\/sup> – 6x + 15y – 16 = 0 intercepted by the y-axis.
\nAnswer:
\ncentre = \\(\\left(3, \\frac{-15}{2}\\right)\\) & C = -16
\nLength of the chord intercepted by y – axis = 2\\(\\sqrt{f^{2}-c}\\) = 2\\(\\sqrt{\\left(\\frac{15}{2}\\right)^{2}+16}\\)
\n\"2nd<\/p>\n

Question 3.
\nFind the length of the chord of the circle x2<\/sup> + y2<\/sup> + 3x – 2 = 0 intercepted by y-axis.
\nAnswer:
\nCentre = \\(\\left(-\\frac{3}{2}, 0\\right)\\) c = -2
\nLength of the chord by y – axis = 2\\(\\sqrt{f^{2}-c}\\) = 2\\(\\sqrt{0+2}\\) = 2\\(\\sqrt{2}\\) units.<\/p>\n

\"KSEEB<\/p>\n

Question 4.
\nFind the length of the chord of the circle x2<\/sup> + y2<\/sup> + 3x – y – 6 = 0 intercepted by the y-axis.
\nAnswer:
\nCentre = \\(\\left(-\\frac{3}{2}, \\frac{1}{2}\\right)\\) c = -6
\nLength of the chord by axis = 2 \\(\\sqrt{f^{2}-c}\\) = 2\\(\\sqrt{\\frac{1}{4}+6}\\) = 2\\(\\sqrt{\\frac{25}{4}}\\) = 5 units<\/p>\n

Question 5.
\nFind the length of the chord of the circle x2<\/sup> + y2<\/sup> + 4x + 6y – 12 = 0 and x + 4y – 6 = 0.
\nAnswer:
\n\"2nd<\/p>\n

Question 6.
\nFind the length of the chord intercepted by the circle x2<\/sup> + y2<\/sup> – 8x – 6y \u2013 6 = 0 and the line x – 7 y – 8 = 0.
\nAnswer:
\n\"2nd<\/p>\n

Question 7.
\nFind the length of the chord intercepted by the circle x2<\/sup> + y2<\/sup> – 6x – 2y + 5 = 0 and the line x – y + 1 = 0.
\nAnswer:
\n\"2nd<\/p>\n

Question 8.
\nProve that the length of the chord x + 2y = 5 of the circle x2<\/sup> + y2<\/sup> = 9 is 4 units.
\nAnswer:
\nLength of the chord intercepted by x – axis = 2\\(\\sqrt{g^{2}-c}\\)
\nHere g = 5, f = -3, c = 9
\n\u2234 Length = \\(2 \\cdot \\sqrt{25-9}=2 \\sqrt{16}\\)
\n= 2(4) = 8 units
\nHence proved.
\nCentre of the given circle = (0,0), r = 3 units line = x + 2y – 5 = 0
\n\\(d=\\left|\\frac{0+2(0)-5}{\\sqrt{1^{2}+2^{2}}}\\right|=\\frac{5}{\\sqrt{5}}=\\sqrt{5}\\)
\n\u2234 Length of the chord = \\(2 \\cdot \\sqrt{r^{2}-d^{2}}\\)
\n\\(=2 \\cdot \\sqrt{(3)^{2}-(\\sqrt{5})^{2}}=2 \\sqrt{9-5}=2.2=4 \\text { units. }\\)
\nHence proved.<\/p>\n

\"KSEEB<\/p>\n

Part – C<\/span><\/p>\n

2nd PUC Basic Maths Circles Ex 15.3 Five Marks Questions and Answers<\/strong><\/p>\n

Question 1.
\nShow that the line 3x + 4y + 7 = 0 touches the circle x2<\/sup> + y2<\/sup> – 4x – 6y – 12 = 0 and find the point of contact.
\nAnswer:
\nGiven centre = (2, 3) and r = \\(\\sqrt{4+9+12}\\) = \\(\\sqrt{25}\\) = 5
\nIf the length of the perpendicular is equal to radius of the circle than the line touches the circle
\n\"2nd
\n\u2234 The line 3x + 4y + 7 touches the circle
\nAny line perpendicular to 3x + 4y + 7 = 0 is of the form 4x – 3y + k = 0
\nIt passes through (2,3) \u2234 8 – 9 + k = 0 \u21d2 k = 1
\n\u2234 The line is 4x – 3y + 1 = 0
\nPoint of contact is the intersection of 3x + 4y + 7 = 0 and 4x – 3y + 1 = 0
\n\"2nd
\n\u2234 The point of contact is (-1,-1)<\/p>\n

Question 2.
\nFind k if the line 3x + y + k = 0 touches the circle x2<\/sup> + y2<\/sup> – 2x – 4y – 5 = 0.
\nAnswer:
\nGiven C = (1, 2) C = -5
\nRadius = Length of the perpendicular from (1, 2) to 3x + y + k = 0.
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 3.
\nFind k if the 2x + y + k = 0 touches the circle x2<\/sup> + y2<\/sup> + 6x + 2y + 5 = 0.
\nAnswer:
\nHence centre = (-3,-1), c = 5
\n\\(r=\\sqrt{g^{2}+f^{2}+c}=\\sqrt{9+1-5}=\\sqrt{5}\\)
\nr = length of the perpendicular from (-3,-1) to the line 2x + y + k = 0
\n\\(r=\\sqrt{g^{2}+f^{2}+c}=\\sqrt{9+1-5}=\\sqrt{5}\\)
\n\"2nd<\/p>\n

Question 4.
\nFind k if the line 4x – y + k = 0 touches the circle x2<\/sup> + y2<\/sup> + 4x – 8y + 3 = 0.
\nAnswer:
\nHere centre = (-2,4), r = \\(\\sqrt{4+16-3}\\) = \\(\\sqrt{17}\\)
\nradius = length of perpendicular from (-2, 4) to the line 4x – y + k = 0
\n\u2234 \\(\\sqrt{17}\\) = \\(\\left|\\frac{4(-2)-4+k}{\\sqrt{16+1}}\\right|\\)
\n-12 + k = \u00b1\\((\\sqrt{17})^{2}\\) \u21d2 -12 + K = \u00b117 \u21d2 k = 28 or -5<\/p>\n

Question 5.
\nFind k such that the line x – 2y + k = 0 touches the circle x2<\/sup> + y2<\/sup> + 3x – 2y + 2 = 0.
\nAnswer:
\nHere centre \\(\\left(-\\frac{3}{2}, 1\\right)\\), \\(r=\\sqrt{\\frac{9}{4}+1-2}=\\sqrt{\\frac{5}{4}}\\)
\nr = length of perpendicular from \\(\\left(-\\frac{3}{2},-1\\right)\\) to the line x – 2y + k = 0
\n\"2nd<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Basic Maths Exercise 15.3 Questions and Answers, Notes Pdf, 2nd PUC Basic Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka 2nd PUC Basic Maths Question Bank Chapter 15 Circles Ex 15.3 Part – A 2nd PUC Basic …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[82],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/20435"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=20435"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/20435\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=20435"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=20435"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=20435"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}