Let lx-2y=1 intersects the parabola y^2=4ax at points P and Q. If PS and QS meet the parabola again at R and T respectively (where S is the focus of…

Question

Let lx-2y=1 intersects the parabola y^2=4ax at points P and Q. If PS and QS meet the parabola again at R and T respectively (where S is the focus of y^2=4ax ), then the slope of RT is equal to

MARKS Content Team · Accepted Answer

Correct answer: 0.5. Let, P=t12,2t_1 and Q=t22,2t_2 Equation of PS is t_1+t_2y=2x+2t_1t_2 ⇒ lines -2x+t_1+t_2y=2t_1t_2 and lx-2y=1 are same ⇒(-2)/l=(t_1+t_2)/(-2)=2t_1t_2/1 ⇒t_1+t_2=4/l & t_1t_2=(-1)/l Now, R=1/t12,(-2)/t_1 and T=1/t22,(-2)/t_2 The slope of RT is (-2)/t_2+2/t_11/t22-1/t12=(-2t_1-t_2)/t_1t_2(t_1-t_2t_1+t_2)/t12t22 =(-2t_1t_2)/(t_1+t_2)=2l/4l=1/2=0.5

Let $l x - 2 y = 1$ intersects the parabola $y^{2} = 4 a x$ at points $P$ and $Q .$ If $P S$ and $Q S$ meet the parabola again at $R$ and $T$ respectively (where $S$ is the focus of $y^{2} = 4 a x$ ), then the slope of $R T$ is equal to

Solution

More Parabola Questions

Let lx-2y=1 intersects the parabola y2=4ax at points P and Q. If PS and QS meet the parabola again at R and T respectively (where S is the focus of y2=4ax ), then the slope of RT is equal to

Solution

More Parabola Questions

Let $l x - 2 y = 1$ intersects the parabola $y^{2} = 4 a x$ at points $P$ and $Q .$ If $P S$ and $Q S$ meet the parabola again at $R$ and $T$ respectively (where $S$ is the focus of $y^{2} = 4 a x$ ), then the slope of $R T$ is equal to