If the tangent at (1,1) on y2=x(2-x)2 meets the curve again at P then the co-ordinates of P are

Question

If the tangent at (1,1) on y2=x(2-x)2 meets the curve again at P then the co-ordinates of P are (A) ((9/4), (3/8)) (B) (3, √3) (C) (4,4) (D) none of these

Tardigrade Admin · Accepted Answer

.( dy / dx )|(1,1)=-(1/2) ; ( y 1-1/ x 1-1)=-(1/2) ; 2 y 1+ x 1=3 which is satisfying option (1)

Q. If the tangent at $(1, 1)$ on $y^{2} = x (2 - x)^{2}$ meets the curve again at $P$ then the co-ordinates of $P$ are

$(\frac{9}{4}, \frac{3}{8})$

$(3, 3)$

$(4, 4)$

none of these

$\frac{d y}{d x} ∣ ∣_{(1, 1)} = - \frac{1}{2}; \frac{y _{1} - 1}{x _{1} - 1} = - \frac{1}{2}; 2 y_{1} + x_{1} = 3$ which is satisfying option (1)

Q. If the tangent at (1,1) on y2=x(2−x)2 meets the curve again at P then the co-ordinates of P are

(49​,83​)

(3,3​)

(4,4)