Question

The equation of the common tangent touching the circle (x - 3 )2 + y2 = 9 and parabola y2 = 4x above the x-axis is:

a) ?3 y = 3x + 1 b) ?3 y = - ( x + 3 )
c) ?3 y = x + 3 d) ?3 y = - (3x + 1 )

Answer 1

3y=3x+1 is write answer

Answer 2

Answer:

Option C is correct.

Step-by-step explanation:

Given:

Equation of Circle, ( x - 3 )² + y² = 9

⇒ x² - 6x + y² = 0

Equation of parabola, y² = 4x

So, Equation of tangent ,T : y  = mx+ a/m

We know equation of parabola is y² = 4ax

So, 4a = 4 ⇒ a = 1.

⇒ y = mx + 1/m

Put, this in equation of circle.

$x^2-6x+(mx+\frac{1}{m})^2=0$

$x^2-6x+(mx)^2+(\frac{1}{m})^2+2\times mx\times\frac{1}{m}=0$

$(1+m^2)x^2-4x+\frac{1}{m^2}=0$

Now, We know that D ( Discriminant ) = 0

⇒ b² - 4ac = 0

$(-4)^2-4(1+m^2)(\frac{1}{m^2})=0$

$16m^2-4(1+m^2)=0$

$4m^2-(1+m^2)=0$

$4m^2-1-m^2=0$

3m² = 1

since slope is above x-axis we take positive value of m.

m = 1/√3

Equation of Common Tangent, T : y = 1/√3 x + 1/(1/√3)

y = x/√3 + √3

√3y = x + 3

Therefore, Option C is correct.