The points $(- 4, 4)$ and $(- 16, b)$ lie on the locus $y^{2} = a x$ . Find the values of $^{'} a^{'}$ and $^{'} b^{'}$ .

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Solution

If both points $(- 4, 4)$ and $(- 16, b)$ lie on the locus $y^{2} = a x$ , then they will satisfy the locus equation.

Substitute $x = - 4$ and $y = 4$ in the locus equation,

$4^{2} = a (- 4)$
$16 = - 4 a$
$a = - 4$

So the locus is $y^{2} = - 4 x$

Substitute $x = - 16$ and $y = b$ in the locus equation,

$b^{2} = - 4 (- 16)$
$b^{2} = 64$
$b = \pm 8$

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The points (−4,4) and (−16,b) lie on the locus y2=ax. Find the values of ′a′ and ′b′.

If both points (−4,4) and (−16,b) lie on the locus y2=ax, then they will satisfy the locus equation.Substitute x=−4 and y=4 in the locus equation,42=a(−4)16=−4aa=−4So the locus is y2=−4xSubstitute x=−16 and y=b in the locus equation,b2=−4(−16)b2=64b=±8

The points $(- 4, 4)$ and $(- 16, b)$ lie on the locus $y^{2} = a x$ . Find the values of $^{'} a^{'}$ and $^{'} b^{'}$ .