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.

Question

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. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Curve is straight line i.e. x+y=3 ∴ P ((3/2), (3/2)) ∴ OP 2=(9/2) ⇒ 2( OP 2)=9

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 $2 (OP)^{2}$ .

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

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.

Curve is straight line i.e. x+y=3 ∴P(23​,23​) ∴OP2=29​⇒2(OP2)=9

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 $2 (OP)^{2}$ .

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