Question

The equation of tangent at t=2 to the parabola y²=8x is​

Answer 1

GIVEN :–

• Parabola is y² = 8x .

• t = 2

TO FIND :–

• Equation of tangent = ?

SOLUTION :–

• We know that standard form of parabola is –

$\\ \bf \implies {y}^{2} = 4ax$

• Now compare –

$\\ \bf \implies a = 2$

• We also know that –

$\\ \bf \implies Points \: \: on \: \: parabola \to(a {t}^{2} , 2at)$

• So that point on parabola –

$\\ \bf \implies Points \: \: on \: \: parabola \to( 2{(2)}^{2} , 2(2)(2))$

$\\ \bf \implies Points \: \: on \: \: parabola \to(8,8)$

• And tangent form –

$\\ \bf \implies y y_{1}= 8(x + x_{1})$

• Here –

$\\ \bf \implies (x_{1},y_{1})\to(8,8)$

• So that –

$\\ \bf \implies y(8)= 8(x +8)$

$\\ \bf \implies y=x +8$

$\\ \large\implies{ \boxed{ \bf x - y + 8 = 0}}$