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In the parabola `y^2=4a x ,`then tangent at `P`whose abscissa is equal to the latus rectum meets its axis at `T ,`and normal `P`cuts the curve again at `Qdot`Show that `P T: P Q=4: 5.`A. `5:4`B. `2:1`C. `3:4`D. `4:5` |
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Answer» Let P be `(at^(2),2at)`. Since `at^(2)=4a`, we have t = 2. Tangent at P is `2y=x+4a`, which meets x-axis at T (-4a,0). If coordinates of Q are `(at_(1)^(2),2at_(1))`, then `t_(1)=-t-(2)/(t)=-3` `:. Q " is " (9a, - 6a)` `:. (PQ)^(2)=125a^(2)` and `(PT)^(2)=80a^(2)` `rArr PT : PQ= 4:5`. |
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