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  4. A curve with negative gradient is passing through R (2,1) and tangent at any point to the curve passes through M (1,2). If normal from origin O intersects the curve at P, then find the value of 2( OP )2.

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Q. A curve with negative gradient is passing through $R (2,1)$ and tangent at any point to the curve passes through $M (1,2)$. If normal from origin $O$ intersects the curve at $P$, then find the value of $2( OP )^2$.

Differential Equations

Solution:

Curve is straight line i.e. $x+y=3$
$\therefore P \left(\frac{3}{2}, \frac{3}{2}\right) $
$\therefore OP ^2=\frac{9}{2} \Rightarrow 2\left( OP ^2\right)=9 $