Q95 / 160 · AP EAMCET 2019 (23 Apr Shift 1) · Mathematics
For any non-zero real value of \(m\), the equation of the parabola to which the line \(m x-y+10+m^2=0\) is a tangent, is
- A\(x^2=y-10\)
- B\(y^2=4(x-2)\)
- Correct answerC\(x^2=-4(y-10)\)
- D\(x^2=-4 y\)
Solution
Given, equation of tangent to the parabola is
\(\begin{aligned}
m x-y+\left(10+m^2\right) & =0 \\
m^2+m x+(10-y) & =0
\end{aligned}\)
Since, above line is tangent, then \(D=0\)
\(\begin{aligned}
b^2-4 a c & =0 \\
x^2-4 \cdot 1 \cdot(10-y) & =0 \\
x^2 & =4(10-y) \\
x^2 & =-4(y-10)
\end{aligned}\)
Hence, answer is (c).
Hence, the correct answer is option: 'C'.