ParabolaHardBloom L3
Question
The points of contact $Q$ and $R$ of tangent from the point $P(2,3)$ on the parabola $y^{2} = 4x$ are:
Options
A.$(9,6)$ and $(1,2)$
B.$(1,2)$ and $(4,4)$
C.$(4,4)$ and $(9,6)$
D.$(9,6)$ and $(1/4,1)$
Solution
Sol. [Key Concept: The points of contact are the intersections of the chord of contact $T = 0$ (here $3y = 2(x + 2)$) with the parabola.]
Equation of tangent at $\left( t^{2},2t \right)$
$$yt = x + t^{2}$$
Put $(2,3) \Rightarrow t^{2} - 3t + 2 = 0$
$$t = 1,2 \Rightarrow Q,R \equiv (1,2)\text{~}\text{and}\text{~}(4,4)$$
Create a free account to view solution
View Solution FreeMore Parabola Questions
The set of points $(x,y)$ whose distance from the line $y = 2x + 2$ is the same as the distance from $(2,0)$ is a parabo...Parabolas $(y - \alpha)^{2} = 4a(x - \beta)$ and $(y - \alpha)^{2} = 4a^{'}\left( x - \beta^{'} \right)$ will ha...Let $y^{2} = 4ax$ be a parabola and $x^{2} + y^{2} + 2bx = 0$ be a circle. If parabola and circle touch each other exter...The vertex of a parabola is at $(3,2)$ and its directrix is the line $x - y + 1 = 0$. Then the equation of its latus rec...Consider ellipse = 1 (a > b) & parabola y2 = 4A(x + 4), A > 0. If vertex of parabola coincideswith one focus of ellipse ...