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  4. Tangents are drawn from the point P (3+4 i ) to the ellipse S :| z +√5|+| z -√5|-6=0 touching the ellipse S at points A and B. The orthocentre of the triangle PAB is

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Q. Tangents are drawn from the point $P (3+4 i )$ to the ellipse $S :| z +\sqrt{5}|+| z -\sqrt{5}|-6=0$ touching the ellipse $S$ at points $A$ and $B$.
The orthocentre of the triangle PAB is

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Solution:

Correct answer is (c) $\frac{11}{5}+\frac{8}{5} i$