Question

if the line passing through the points (-1, 10) and (0,6) is tangent to the curve y=-c^2/(x-1), c^2is equal to ?​

Answer 1

Slop of line joining the points (0,3)and(5,2) is given by

$\binom{32 + 2} +{0 - 5} = - 1$

This is equal to the slop of tangent on the curve and that is given by

$\binom{dy}{dx} = \binom{ - c}{x + 1}$

$\binom{dy}{dx} = - 1$

$⇒c=(x+ {1}^{2} )$

Equation of line joining the points (0,3)and(5,2) is given by

(y−3)=−1(x−0)

Solving equation of tangent and the curve for point of intersection

$\binom{c}{x + 1} + x = 2$

Solving (1) and (2)

$x=1$

Putting this in (2), we get c=4

answer=c4

Answer 2

Answer:

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