Parabola Ques 52
- Match the conditions/expressions in Column I with statement in Column II. Normals at $P, Q, R$ are drawn to $y^{2}=4 x$ which intersect at $(3,0)$. Then,
| Column 1 | Column 2 |
|---|---|
| A. Area of $\triangle P Q R$ | p. 2 |
| B. Radius of circumcircle of $\triangle P Q R$ | q. $\frac{5}{2}$ |
| C. Centroid of $\triangle P Q R$ | r. $\frac{5}{2}, 0$ |
| D. Circumcentre of $\triangle P Q R$ | s. $\frac{2}{3}$, $0$ |
Objective Questions II
(One or more than one correct option)
Show Answer
Answer:
Correct Answer: 52.$A \rightarrow p ; B \rightarrow q ; C \rightarrow s ; D \rightarrow r$
Solution:
- Equation of chord with mid-point $(h, k)$.
$$ \begin{array}{rlrl} T &=S_1 \ y(k-8)(x-8)h & =k^{2}-16 h \\ 2 x-\frac{y k}{4} & =2 h-\frac{k^{2}}{4} \\ \because \quad 2x+y & =p \\ \therefore & k & =-4 \text { and } p=2 h-4 \\ \text { where } \quad h & =3 \\ & p & =2 \times (3-4)= -2 \end{array} $$
BETA
