The tangent at a point P on the parabola $$y2$$ $$=$$ $$8x$$ meets the directrix of the parabola at Q such that distance of Q from the axis of the parabola is $$3$$. Then the coordinates of P cannot be

Question

The tangent at a point P on the parabola $$y2$$ $$=$$ $$8x$$ meets the directrix of the parabola at Q such that  distance of Q from the axis of the parabola is $$3$$. Then the coordinates of P cannot be

Infinity Learn · Accepted Answer

Equation of the tangent at  P (2t2$$ , $$4t) to the parabola is ty $$=$$ x $$+$$ $$2t$$ $$2$$ which meets the directrix x $$=$$–$$2$$ of the parabola at Q for which $$y=2t2$$−$$2t$$. So that $$2t2$$−$$2t=$$±$$3$$.⇒$$2t2$$−$$3t$$−$$2=0$$ or  $$2t2+3t$$−$$2=0$$⇒(2t+1)(t$$−$$2)=0$$ or  $$(2t$$−$$1)(t+2)=0$$⇒$$t=$$±$$2$$,±$$12So$$, the coordinates of P are $$(8$$,±$$8) or  $$12$$,±$$2$$

The tangent at a point $P$ on the parabola $y^{2} = 8 x$
meets the directrix of the parabola at $Q$ such that
distance of $Q$ from the axis of the parabola is 3.
Then the coordinates of $P$ cannot be

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The tangent at a point P on the parabola y2 = 8x meets the directrix of the parabola at Q such that distance of Q from the axis of the parabola is 3. Then the coordinates of P cannot be

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Ready to Test Your Skills?

free study material

The tangent at a point $P$ on the parabola $y^{2} = 8 x$
meets the directrix of the parabola at $Q$ such that
distance of $Q$ from the axis of the parabola is 3.
Then the coordinates of $P$ cannot be