Two tangents are drawn from a point (- 2, -1) to the curve, y2=4x. If α is the angle between them, then | tan α| is equal to :

Question

Two tangents are drawn from a point (- 2, -1) to the curve, y2=4x. If α is the angle between them, then | tan α| is equal to : (A) (1/3) (B) (1/√3) (C) √3 (D) 3

Tardigrade Admin · Accepted Answer

Let equation of tangent from (-2,-1) be y +1= m ( x +2) ⇒ y = m x +(2 m -1) Condition of tangency, C =( a / m ) i.e., 2 m -1=(1/ m ) ⇒ 2 m 2- m -1=0 (2 m +1)( m -1)=0 m =-(1/2), 1 Now, | tan α|=|( m 1- m 2/1+ m 1 m 2)| =|(1+(1/2)/1-(1)2)|=3

Q. Two tangents are drawn from a point $(- 2, - 1)$ to the curve, $y^{2} = 4 x .$ If $α$ is the angle between them, then $∣ tan α ∣$ is equal to :

$\frac{1}{3}$

$\frac{1}{3}$

$3$

$3$

Q. Two tangents are drawn from a point (−2,−1) to the curve, y2=4x. If α is the angle between them, then ∣tanα∣ is equal to :

31​

3​1​

3​

3

Let equation of tangent from (−2,−1) be y+1=m(x+2) ⇒y=mx+(2m−1) Condition of tangency, C=ma​ i.e., 2m−1=m1​ ⇒2m2−m−1=0 (2m+1)(m−1)=0 m=−21​,1 Now, ∣tanα∣=∣∣​1+m1​m2​m1​−m2​​∣∣​ =∣∣​1−21​1+21​​∣∣​=3

Q. Two tangents are drawn from a point $(- 2, - 1)$ to the curve, $y^{2} = 4 x .$ If $α$ is the angle between them, then $∣ tan α ∣$ is equal to :

$\frac{1}{3}$

$\frac{1}{3}$

$3$

$3$