Ellipse 3 Question 2
2. The orthocentre of the $\triangle P A B$ is
(a) $5, \frac{8}{7}$
(b) $\frac{7}{5}, \frac{25}{8}$
(c) $\frac{11}{5}, \frac{8}{5}$
(d) $\frac{8}{25}, \frac{7}{5}$
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Answer:
Correct Answer: 2. (c)
Solution:
- Equation of $A B$ is
$$ \begin{aligned} y-0 & =\frac{\frac{8}{5}}{-\frac{9}{5}-3}(x-3)=\frac{8}{-24}(x-3) \\ \Rightarrow \quad & =-\frac{1}{3}(x-3) \\ \Rightarrow \quad x+3 y & =3 \end{aligned} $$
Equation of the straight line perpendicular to $A B$ through $P$ is
$$ 3 x-y=5 $$
Equation of $P A$ is $2 x-3=0$
The equation of straight line perpendicular to $P A$ through $B \frac{-9}{5}, \frac{8}{5}$ is $y=\frac{8}{5}$.
Hence, the orthocentre is $\frac{11}{5}, \frac{8}{5}$.
