If the normal to the parabola y2=4 ax at the point with parameter t1, cuts the parabola again at the point with parameter t2, then

Question

If the normal to the parabola y2=4 ax at the point with parameter t1, cuts the parabola again at the point with parameter t2, then (A) 2 ≤ t22 ≤ 8 (B) 2 ≤ t22 ≤ 4 (C) t 22 ≥ 4 (D) t 22 ≥ 8

Tardigrade Admin · Accepted Answer

t2=-(t1+(2/t1)) ; t22=((2/t1)+t1)2=((2/t1)-t1)2+8 ⇒ t22 ≥ 8

Q. If the normal to the parabola $y^{2} = 4 a x$ at the point with parameter $t_{1}$ , cuts the parabola again at the point with parameter $t_{2}$ , then

$2 \leq t_{2}^{2} \leq 8$

$2 \leq t_{2}^{2} \leq 4$

$t_{2}^{2} \geq 4$

$t_{2}^{2} \geq 8$

$t_{2} = - (t_{1} + \frac{2}{t _{1}}); t_{2}^{2} = (\frac{2}{t _{1}} + t_{1})^{2} = (\frac{2}{t _{1}} - t_{1})^{2} + 8 \Rightarrow t_{2}^{2} \geq 8$

Q. If the normal to the parabola y2=4ax at the point with parameter t1​, cuts the parabola again at the point with parameter t2​, then

2≤t22​≤8

2≤t22​≤4

t22​≥4

t22​≥8