If tangent at (1,2) to the circle c1: x2+y2=5 intersects the circle c2: x2+y2=9 at A B and tangents at A B to the second circle meet at point C, then the co-ordinates of C are:

Question

If tangent at (1,2) to the circle c1: x2+y2=5 intersects the circle c2: x2+y2=9 at A B and tangents at A B to the second circle meet at point C, then the co-ordinates of C are: (A) (4,5) (B) ((9/15), (18/5)) (C) (4,-5) (D) ((9/5), (18/5))

Tardigrade Admin · Accepted Answer

Tangent at (1,2) to the circle x2+y2=5 x+2 y-5=0 chord of contact from C(h, k) to x2+y2=9 h x+k y-9=0 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/af3d5f0dc9284d184e510077d04ad8e8-.png" /> compare both equations ( h /1)=( k /2)=(9/5) (h, k) ≡((9/5), (18/5))

Q. If tangent at $(1, 2)$ to the circle $c_{1} : x^{2} + y^{2} = 5$ intersects the circle $c_{2} : x^{2} + y^{2} = 9$ at $A$ & $B$ and tangents at $A & B$ to the second circle meet at point $C$ , then the co-ordinates of $C$ are:

$(4, 5)$

$(\frac{9}{15}, \frac{18}{5})$

$(4, - 5)$

$(\frac{9}{5}, \frac{18}{5})$

Tangent at $(1, 2)$ to the circle $x^{2} + y^{2} = 5$
$x + 2 y - 5 = 0$
chord of contact from $C (h, k)$ to $x^{2} + y^{2} = 9$
$h x + k y - 9 = 0$

compare both equations $\frac{h}{1} = \frac{k}{2} = \frac{9}{5}$
$(h, k) \equiv (\frac{9}{5}, \frac{18}{5})$

Q. If tangent at (1,2) to the circle c1​:x2+y2=5 intersects the circle c2​:x2+y2=9 at A & B and tangents at A&B to the second circle meet at point C, then the co-ordinates of C are:

(4,5)

(159​,518​)

(4,−5)

(59​,518​)