If the line y =4+ kx , k 0, is the tangent to the parabola y = x - x 2 at the point P and V is the vertex of the parabola, then the slope of the line through P and V is

Question

If the line y =4+ kx , k >0, is the tangent to the parabola y = x - x 2 at the point P and V is the vertex of the parabola, then the slope of the line through P and V is (A) (3/2) (B) (26/9) (C) (5/2) (D) (23/6)

Tardigrade Admin · Accepted Answer

Slope of tangent at P= Slope of line AP .y prime|P=1-2 α=(α-α2-4/α) Solving α=-2 ⇒ P(-2,-6) Slope of PV=(5/2)

Q. If the line $y = 4 + k x, k > 0$ , is the tangent to the parabola $y = x - x^{2}$ at the point $P$ and $V$ is the vertex of the parabola, then the slope of the line through $P$ and $V$ is

$\frac{3}{2}$

$\frac{26}{9}$

$\frac{5}{2}$

$\frac{23}{6}$

Slope of tangent at $P =$ Slope of line $A P$
$y^{'} ∣_{P} = 1 - 2 α = \frac{α - α ^{2} - 4}{α}$
Solving $α = - 2 \Rightarrow P (- 2, - 6)$
Slope of $P V = \frac{5}{2}$

Q. If the line y=4+kx,k>0, is the tangent to the parabola y=x−x2 at the point P and V is the vertex of the parabola, then the slope of the line through P and V is

23​

926​

25​

623​