SATHEE: Circle 2 Question 19

Circle 2 Question 19

20. A line $M$ through $A$ is drawn parallel to $B D$ . Point $S$ moves such that its distances from the line $B D$ and 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 $Δ T_{1} T_{2} T_{3}$ is

(a) $\frac{1}{2}$ sq unit

(b) $\frac{2}{3}$ sq unit

(d) 2 sq units

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Answer:

Correct Answer: 20. (c)

Solution:

Since,

$A G = \sqrt{2}$

$∴ A T_{1} = T_{1} G = \frac{1}{\sqrt{2}}$

As, $A$ is the focus, $T_{1}$ is the vertex and $B D$ is the directrix of parabola.

Also, $T_{2} T_{3}$ is latusrectum.

$\begin{array}{ll} ∴ T_{2} T_{3} = 4 \cdot \frac{1}{\sqrt{2}} \\ ∴ Area of Δ T_{1} T_{2} T_{3} = \frac{1}{2} \times \frac{1}{\sqrt{2}} \times \frac{4}{\sqrt{2}} = 1 sq unit \end{array}$

Circle 2 Question 19

20. A line $M$ through $A$ is drawn parallel to $B D$ . Point $S$ moves such that its distances from the line $B D$ and 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 $Δ T_{1} T_{2} T_{3}$ is

Answer:

Solution:

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Circle 2 Question 19

20. A line M through A is drawn parallel to BD. Point S moves such that its distances from the line BD and the vertex A are equal. If locus of S cuts M at T2 and T3 and AC at T1, then area of ΔT1T2T3 is

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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20. A line $M$ through $A$ is drawn parallel to $B D$ . Point $S$ moves such that its distances from the line $B D$ and 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 $Δ T_{1} T_{2} T_{3}$ is