Parabola 3 Question 3
3. 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 I | Column II |
|---|---|
| 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)
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Answer:
Correct Answer: 3. $A \rightarrow p ; B \rightarrow q ; C \rightarrow s ; D \rightarrow r$
Solution:
- Equation of chord with mid-point $(h, k)$.
$$ \begin{array}{rlrl} T & =S _1 \\ y k-8 x-8 h & =k^{2}-16 h \\ 2 x-\frac{y k}{4} & =2 h-\frac{k^{2}}{4} \\ \because \quad 2 x+y & =p \\ \therefore & k & =-4 \text { and } p=2 h-4 \\ \text { where } \quad h & =3 \\ & p & =2 \times 3-4=2 \end{array} $$
