The chord AB of the parabola y2-4ax cuts the axis of the parabola at C - If A- at21-2at1 -B- at22-2at2 and AC-AB-1-3 then

The correct option is B t_2+2t_1=0 AC:AB=1:3 ⇒ BC:AC=2:1 Using section formula C=( 2a t _ 1 ^ 2 +a t _ 2 ^ 2 3 , 4a t _ 1 +2a t _ 2 3 ...

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Standard XII

Mathematics

Directrix of Hyperbola

The chord A...

Question

The chord $A B$ of the parabola $y^{2} = 4 a x$ cuts the axis of the parabola at $C$ . If $A = (a t_{1}^{2}, 2 a t_{1}), B = (a t_{2}^{2}, 2 a t_{2})$ and $A C : A B = 1 : 3$ then

t_{2} = 2 t_{1}

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t_{2} + 2 t_{1} = 0

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t_{1} + 2 t_{2} = 0

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Solution

The correct option is B $t_{2} + 2 t_{1} = 0$
$A C : A B = 1 : 3$
$\Rightarrow B C : A C = 2 : 1$
Using section formula $C = (\frac{2 a {t_{1}}^{2} + a {t_{2}}^{2}}{3}, \frac{4 a t_{1} + 2 a t_{2}}{3})$
Since, this lies on axis of parabola
Therefore, $\frac{4 a t_{1} + 2 a t_{2}}{3} = 0$
$\Rightarrow t_{2} + 2 t_{1} = 0$

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Similar questions

The chord AB of the parabola $y^{2} = 4 a x$ cuts the axis of the parabola at C. If $A = (a t_{1}^{2}, 2 a t_{1}), B = (a t_{2}^{2}, 2 a t_{2})$ and AC : AB = 1:3 then

Q. If

P Q

is a normal chord of the parabola

y^{2} = 4 a x

P (a t^{2}, 2 a t) .

Then the axis of the parabola divides

¯ ¯¯¯¯¯¯ ¯ P Q

in the ratio

Q. If the coordinates of the Parabola of the ends of a focal chord of Parabola

y^{2} = 4 a x

are

(a t_{1}^{2}, 2 a t_{1})

and

(a t_{2}^{2}, 2 a t_{2})

, then prove that :

t_{1} . t_{2} = - 1

If the chord joining the points $(a t_{1}^{2}, 2 a t_{1})$ and $(a t_{2}^{2}, 2 a t_{2})$ of the parabola $y^{2} = 4 a x$ passes through the focus of the parabola, then

Q. If

t_{1}

and

t_{2}

are the extremities of any focal chord of the parabola

y^{2} = 4 a x

then

t_{1} t_{2} =

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The chord AB of the parabola y2=4ax cuts the axis of the parabola at C . If A=(at21,2at1),B=(at22,2at2) and AC:AB=1:3 then

The correct option is B t2+2t1=0AC:AB=1:3⇒BC:AC=2:1Using section formula C=(2at12+at223,4at1+2at23)Since, this lies on axis of parabola Therefore, 4at1+2at23=0⇒t2+2t1=0

The chord $A B$ of the parabola $y^{2} = 4 a x$ cuts the axis of the parabola at $C$ . If $A = (a t_{1}^{2}, 2 a t_{1}), B = (a t_{2}^{2}, 2 a t_{2})$ and $A C : A B = 1 : 3$ then