Two mutually perpendicular tangents of the parabola y^2=4ax at the points Q_1 and Q_2 on it meet its axis in P_1 and P_2. If S is the focus of the…

Question

Two mutually perpendicular tangents of the parabola y^2=4ax at the points Q_1 and Q_2 on it meet its axis in P_1 and P_2. If S is the focus of the parabola, then the value of 1^(SP1+1SP2-1) is equal to

MARKS Content Team · Accepted Answer

Correct answer: (C) a. Let Q_1=at12,2at_1 & Q_2=at22,2at_2 are points of contact of the tangents passing through P_1 & P_2 respectively. ⇒P_1=-at12,0 & P_2=-at22,0 ⇒P_1S=a+at12 & P_2S=a+at22 ⇒1/PS_1+1/PS_2=1/(a+at12)+1/(a+at22)=1/(a+at12)+1/(a+a-1^t12) =1/a

Two mutually perpendicular tangents of the parabola $y^{2} = 4 a x$ at the points $Q_{1}$ and $Q_{2}$ on it meet its axis in $P_{1}$ and $P_{2} .$ If $S$ is the focus of the parabola, then the value of ${(\frac{1}{S P_{1}} + \frac{1}{S P_{2}})}^{- 1}$ is equal to

Solution

More Parabola Questions

Two mutually perpendicular tangents of the parabola y2=4ax at the points Q1 and Q2 on it meet its axis in P1 and P2. If S is the focus of the parabola, then the value of 1SP1+1SP2-1 is equal to

Solution

More Parabola Questions

Two mutually perpendicular tangents of the parabola $y^{2} = 4 a x$ at the points $Q_{1}$ and $Q_{2}$ on it meet its axis in $P_{1}$ and $P_{2} .$ If $S$ is the focus of the parabola, then the value of ${(\frac{1}{S P_{1}} + \frac{1}{S P_{2}})}^{- 1}$ is equal to