Conic Section
1 Board Maths previous year questions on Conic Section — options free on every question; 1 include the answer & explanation free, the rest unlock with PYQ Pass.
Let x2 + y2 + Ax + By + C = 0 be a circle passing through (0, 6) and touching the parabola y = x2 at (2, 4). Then A + C is equal to
[JEE Main 2022, 24 Jun (Shift 1)]
16
\[ \begin{aligned} & x^{2}+y^{2}+A x+B y+C=0 \\ & \Rightarrow 6 B+C=-36 \end{aligned} \]
The tangent of the parabola \( y=x^{2} \) at \( (2,4) \) is
\[ 4 x-y-4=0 \]
The tangent of circle \( x^{2}+y^{2}+A x+B y+C=0 \) at
\( (2,4) \) is
\[ (4+A) x+(8+B) y+2 A+4 B+2 C=0 \]
From equation (1) and (2)
\[ \begin{aligned} & \frac{4+A}{4}=\frac{8+B}{-1}=\frac{2 A+4 B+2 C}{-4} \\ & A+4 B=-36 \\ & 3 A+4 B+2 C=-4 \end{aligned} \]
From equation (3) and (4)
\[ A+C=16 \]
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