If radius of circle passing through the focus of parabola x2=4 y and touches it at M(6,9) is p √10(p ∈ N), then find p.

Question

If radius of circle passing through the focus of parabola x2=4 y and touches it at M(6,9) is p √10(p ∈ N), then find p. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

(x-6)2+(y-9)2+λ(3 x-y-9)=0 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/a2015d11c4c4cc0e17ddf5d885dd20c0-.png" /> Satisfy (0,1) gives λ=10 ⇒ x2+y2+18 x-28 y+27=0, r=5 √10 ⇒ p=5

Q. If radius of circle passing through the focus of parabola $x^{2} = 4 y$ and touches it at $M (6, 9)$ is $p 10 (p \in N)$ , then find $p$ .

$(x - 6)^{2} + (y - 9)^{2} + λ (3 x - y - 9) = 0$

Satisfy $(0, 1)$ gives $λ = 10$
$\Rightarrow x^{2} + y^{2} + 18 x - 28 y + 27 = 0, r = 510$
$\Rightarrow p = 5$

Q. If radius of circle passing through the focus of parabola x2=4y and touches it at M(6,9) is p10​(p∈N), then find p.

(x−6)2+(y−9)2+λ(3x−y−9)=0 Satisfy (0,1) gives λ=10 ⇒x2+y2+18x−28y+27=0,r=510​ ⇒p=5

Q. If radius of circle passing through the focus of parabola $x^{2} = 4 y$ and touches it at $M (6, 9)$ is $p 10 (p \in N)$ , then find $p$ .

$(x - 6)^{2} + (y - 9)^{2} + λ (3 x - y - 9) = 0$

Satisfy $(0, 1)$ gives $λ = 10$
$\Rightarrow x^{2} + y^{2} + 18 x - 28 y + 27 = 0, r = 510$
$\Rightarrow p = 5$