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JEE Main 20154 April
Exam
JEE Main
Year
2015
Date
4 April
Subject
Mathematics
Chapter
Circle

JEE Main 2015 · 4 April · Mathematics · Circle

The number of common tangents to the circles x ^ 2 + y ^ 2 - 4 x -...

The number of common tangents to the circles x2+y2−4x−6y−12=0{x}^{2} + {y}^{2} - 4 x - 6 y - 1 2 = 0 and x2+y2+6x+18y+26=0{x}^{2} + {y}^{2} + 6x + 18y + 26 = 0, is

Options

  1. A44
  2. B11
  3. C22
  4. D33

Correct answer

D. 33

Step-by-step solution

Given x2+y2−4x−6y−12=0{x}^{2} + {y}^{2} - 4 x - 6 y - 1 2 = 0

C1(2,3),r1=22+32+12=25=5{C}_{1}\left(2, 3\right), {r}_{1} = \sqrt{{2}^{2} + {3}^{2} + 12} = \sqrt{25} = 5

And x2+y2+6x+18y+26=0{x}^{2} + {y}^{2} + 6x + 18y + 26 = 0

C2(−3,−9),r2=32+92−26{C}_{2}\left(- 3, - 9\right),{r}_{2} = \sqrt{{3}^{2} + {9}^{2} - 26}

=90−26=8= \sqrt{90 - 26} = 8

Then, C1C2=52+122=13{C}_{1}{C}_{2} = \sqrt{{5}^{2} + 1{2}^{2}} = 13

C1C2=r1+r2{C}_{1}{C}_{2} = {r}_{1} + {r}_{2}

⇒⇒Externally touching circles.

⇒3⇒ 3 common tangents.
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