Question

The angle of intersection of the curves x² = 4y and y² = 4x at point (0, 0) is

1. 0°
2. 30°
3. 45°
4. 90°

Answer 1

Correct Answer - Option 4 : 90°

Given curve

x² = 4y                                   ……(i)

y² = 4x                                   ……(ii)

\(2x = 4\frac{{dy}}{{dx}}\)

At point (0,0)

\({\left( {\frac{{dy}}{{dx}}} \right)_{\left( {0,0} \right)}} = \infty = {m_2}\)

Let \({m_2} = \frac{1}{{m'}}\) 

where m’ = 0

\(\tan \theta = \left| {\frac{{{m_1} - {m_2}}}{{1 + {m_1}{m_2}}}} \right| = \left| {\frac{{{m_1}m' - 1}}{{m' + {m_1}}}} \right| = \left| {\frac{{0 - 1}}{{0 + 0}}} \right|\)

\(\Rightarrow \theta = \frac{\pi }{2} = 90^\circ \;\)