Q92 / 160 · AP EAMCET 2024 (20 May Shift 2) · Mathematics

Equation of a tangent line of the parabola $y^2=8 x$, which passes through the point $(1,3)$ is

Correct answer
A
$y=2 x+1$
B
$2 y=x+5$
C
$y=-2 x+5$
D
$2 y=3 x+3$

Solution

Equation of tangent to parabola $y^2=8 x$ is $y=m x+\frac{2}{m}$
It passes through $(1,3)$ $\Rightarrow 3=m+\frac{2}{m} \Rightarrow m=1,2$ $\therefore$ Tangents are $y=x+2$ and $y=2 x+1$

Hence, the correct answer is option: 'A'.

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