Let $A (9, - 6), B (1, 2)$ and $C (4, 4)$ be three points on the parabola $y^{2} = 4 x .$ The equation of the circumcircle formed by the point of intersections of the tangents at $A, B$ and $C$ is $x^{2} + y^{2} + k x - k y + h = 0.$ Then the value of $k + h$ is

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Solution

The correct option is C $- 1$
The circumcircle formed by the point of intersection of the tangents at any three points on the parabola always passes through the focus of the parabola.
$\Rightarrow 1 + 0 + k - 0 + h = 0 \Rightarrow k + h = - 1$

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Let A(9,−6),B(1,2) and C(4,4) be three points on the parabola y2=4x. The equation of the circumcircle formed by the point of intersections of the tangents at A,B and C is x2+y2+kx−ky+h=0. Then the value of k+h is

The correct option is C −1The circumcircle formed by the point of intersection of the tangents at any three points on the parabola always passes through the focus of the parabola. ⇒1+0+k−0+h=0⇒k+h=−1

Let $A (9, - 6), B (1, 2)$ and $C (4, 4)$ be three points on the parabola $y^{2} = 4 x .$ The equation of the circumcircle formed by the point of intersections of the tangents at $A, B$ and $C$ is $x^{2} + y^{2} + k x - k y + h = 0.$ Then the value of $k + h$ is

The correct option is C $- 1$
The circumcircle formed by the point of intersection of the tangents at any three points on the parabola always passes through the focus of the parabola.
$\Rightarrow 1 + 0 + k - 0 + h = 0 \Rightarrow k + h = - 1$