Question

The equation of the tangent at the point (2, 3) on the curve y= ax' + b is y= 4x - 5. Find
the values of a and b.
have, y = ax? + b​

Answer 1

CORRECT ANSWER.

The Equation of the tangent at point (2,3) on

the curve y² = ax³ + b is y = 4x - 5.Find the

value of a and b.

EXPLANATION.

Equation of tangent at point (2,3).

on the curve y² = ax³ + b is y = 4x - 5.

Differentiate w.r.t to x we get,

→ y² = ax³ + b

→ 2y.dy/dx = 3ax².

→ dy/dx = 3ax²/2y.

→ dy/dx = 3a(2)²/2(3).

→ dy/dx = 12a/6.

→ dy/dx = 2a.

Equation of tangent.

$\sf \: \implies \: (y - y_{1}) = m(x - x_{1})$

→ ( y - 3) = 2a(x - 2).

→ y - 3 = 2ax - 4a.

→ y = 2ax - 4a + 3 .......(1)

→ y = 4x - 5 .........(2)

Compare equation (1) and (2) we get,

→ 2a = 4.

→ a = 2.

→ 3 - 4a = -5.

→ -4a = -5 - 3.

→ a = -8/-4.

→ a = 2.

Put the value of a = 2 in equation (2) we get,

→ y² = ax³ + b.

→ (3)² = 2(2)³ + b.

→ 9 = 16 + b.

→ b = -7.

→ Value of A = 2 and B = -7.