Search any question & find its solution
Question:
Answered & Verified by Expert
Paragraph:
Read the following passage and answer the questions.
Let $A B C D$ be a square of side length 2 units. $C_2$ is the circle through vertices $A, B, C, D$ and $C_1$ is the circle touching all the sides of square $A B C D$. $L$ is the line through $A$.Question:
A line $M$ through $A$ is drawn parallel to $B D$. Points $S$ moves such that its distances from the line $B D$ are the vertex $A$ are equal. If locus of $S$ cuts $M$ at $T_2$ and $T_3$ and $A C$ at $T_1$, then area of $\Delta T_1 T_2 T_3$ is
Options:
Read the following passage and answer the questions.
Let $A B C D$ be a square of side length 2 units. $C_2$ is the circle through vertices $A, B, C, D$ and $C_1$ is the circle touching all the sides of square $A B C D$. $L$ is the line through $A$.Question:
A line $M$ through $A$ is drawn parallel to $B D$. Points $S$ moves such that its distances from the line $B D$ are the vertex $A$ are equal. If locus of $S$ cuts $M$ at $T_2$ and $T_3$ and $A C$ at $T_1$, then area of $\Delta T_1 T_2 T_3$ is
Solution:
2049 Upvotes
Verified Answer
The correct answer is:
1 sq unit
1 sq unit
$\because \quad A G=\sqrt{2}$
$$
\therefore \quad A T_1=T_1 G=\frac{1}{\sqrt{2}}
$$
\{ as $A$ is the focus, $T_1$ is the vertex and $B D$ is the directrix of parabola.\}
Also, $T_2 T_3$ is latus rectum
$$
\begin{aligned}
& \therefore \quad T_2 T_3=4 \cdot \frac{1}{\sqrt{2}} \\
& \therefore \text { Area of } \Delta T_1 T_2 T_3=\frac{1}{2} \times \frac{1}{\sqrt{2}} \times \frac{4}{\sqrt{2}}=1 \text { sq unit }
\end{aligned}
$$
$$
\therefore \quad A T_1=T_1 G=\frac{1}{\sqrt{2}}
$$
\{ as $A$ is the focus, $T_1$ is the vertex and $B D$ is the directrix of parabola.\}
Also, $T_2 T_3$ is latus rectum
$$
\begin{aligned}
& \therefore \quad T_2 T_3=4 \cdot \frac{1}{\sqrt{2}} \\
& \therefore \text { Area of } \Delta T_1 T_2 T_3=\frac{1}{2} \times \frac{1}{\sqrt{2}} \times \frac{4}{\sqrt{2}}=1 \text { sq unit }
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.