A line passing through the point $\mathrm{A}(-2,0)$, touches the parabola $P: y^2=x-2$ at the point $B$ in the first quadrant. The area, of the region bounded by the line AB , parabola P and the x -axis, is :-

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Aicharya · Accepted Answer

Tangent $\begin{aligned} & y=m(x+2) \ & y^2=x-2 \ & (m(n+2))^2=n-2 \ & m^2 x^2+\left(4 m^2-1ight) x+\left(4 m^2+2ight)=0 \ & D=0 \ & \left(4 m^2-1ight)^2-4 m^2\left(4 m^2+2ight)=0 \ & m=\frac{1}{4} \ & y=\frac{1}{4}(n+2) \end{aligned}$ and point of tangency $(6,2)$ $\begin{aligned} & 	ext { Area } A=\int_0^2\left(\left(y^2+2ight)-(4 y-2)ight) d y \ & A=\frac{8}{3} \end{aligned}$ option (3) ~

A line passing through the point $\mathrm{A}(-2,0)$, touches the parabola $P: y^2=x-2$ at the point $B$ in…

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