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

Question

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 (A) 5+(8/7) i (B) (7/5)+(25/8) i (C) (11/5)+(8/5) i (D) (8/25)+(7/5) i

Tardigrade Admin · Accepted Answer

Correct answer is (c) (11/5)+(8/5) i

Q. 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

$5 + \frac{8}{7} i$

$\frac{7}{5} + \frac{25}{8} i$

$\frac{11}{5} + \frac{8}{5} i$

$\frac{8}{25} + \frac{7}{5} i$

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

Q. Tangents are drawn from the point P(3+4i) 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

5+78​i

57​+825​i

511​+58​i

258​+57​i