The equation of the common tangent touching the circle and the parabola y^2 =4x above the X-axis is

JEE MainMathematicsModerateParabola

The equation of the common tangent touching the circle
$(x - 3)^{2} + y^{2} = 9\$ and the parabola
y^2 =4x above the X-axis is

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The equation of tangent to the given parabola having slope m is
mizo.krk ds fn, x,

y = mx + \frac{1}{m}

........( i)
The equation of tangent to the given circle having slope m is
mizo.krk ds fn, x, o`r

y = m(x - 3) \pm 3\sqrt{1 + m^{2}}

Equations (i) and (ii) are identical, So,
(i) o (ii) lehdj.k loZle gSA blfy,

\frac{1}{m} = - 3m \pm 3\sqrt{1 + m^{2}}

Or;k

1 + 3m^{2} = \pm 3m\sqrt{1 + m^{2}}

Or;k

1 + 6m^{2} + 9m^{4} = 9\left( m^{2} + m^{4} \right)

Or;k

3m^{2} = 1

Or;k

m = \pm \frac{1}{\sqrt{3}}

Source: Grass-G / M-26 Mathematics Paper 1 15 Jan.docx

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