Q13 of 462 Page 22

The slope of the tangent at a point P(x, y) on a curve is If the curve passes through the point (3, – 4), find the equation of the curve.

Given the slope of the tangent =

We know that slope of tangent =


∴


⇒


Integrating both sides,


⇒


⇒


⇒


⇒ ……(1)


Now, the curve passes through (3, – 4)


So, it must satisfy the above equation


∴


⇒ ( – 4)2 + (3)2 = c1


⇒ 16 + 9 = c1


⇒ c1 = 25


Putting the value of c1 in equation (1)


∴


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