If the curves $y = x^{2} - 1, y = 8 x - x^{2} - 9$ touch each other at (2, 3) then equation of the common tangent is

4 x - y = 5

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4 x + y = 5

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x - 4 y = 5

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x + 4 y = 14

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Solution

The correct option is A $4 x - y = 5$
$y_{1}^{1} = 2 x$
$y_{2}^{1} = 8 - 2 x$
at the tangent point slope will be
some.
$2 x = 8 - 2 x$
$4 x = 8$
$x = 2$
$y = 3$
$y^{1} = 4$
$(y - 3) = 4 (x - 2)$
$y = 4 x - 5$

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The equation of the circle which intersects circles $x^{2} + y^{2} + x + 2 y + 3 = 0, x^{2} + y^{2} + 2 x + 4 y + 5 = 0$ and

$x^{2} + y^{2} - 7 x - 8 y - 9 = 0$ at right angle, will be

4 x^{2} + 9 y^{2} - 8 x - 36 y + 15 = 0

min (x^{2} - 2 x + y^{2} - 4 y + 5) + max (x^{2} - 2 x + y^{2} - 4 y + 5)

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