You visited us 23 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Sum of Infinite Terms of a GP

A line m thro...

Question

A line m through A is drawn parallel to BD. A point S moves such that its distances from BD and the vertex A are equal. If the locus of S cuts the line m at $T_{2}$ and $T_{3},$ and AC at $T_{1}$ then ar $(△ T_{1} T_{2} T_{3})$ in square units is

\frac{1}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{2}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C 1
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
$∴ T_{2} T_{3} = 4. \frac{1}{\sqrt{2}}$
Therefore area $T_{1} T_{2} T_{3} = \frac{1}{2} \times \frac{1}{\sqrt{2}} \times \frac{4}{\sqrt{2}} = 1$

Suggest Corrections

Similar questions

Q. 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

T_{2}

and

T_{3}

and AC at

T_{1}

, then area of

Δ T_{1} T_{2} T_{3}

Q. 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 the square

A B C D .

L

is a line through

A .

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

T_{2}

and

T_{3}

and

A C

T_{1}

, then area of

Δ T_{1} T_{2} T_{3}

What is the ratio $\frac{A C}{B C}$ for the following construction:
A line segment AB is drawn.
A single ray is extended from A and 12 arcs of equal lengths are cut, cutting the ray at $A_{1}, A_{2} \dots A_{12}$ .
A line is drawn from $A_{12}$ to B and a line parallel to $A_{12} B$ is drawn, passing through the point $A_{6}$ and cutting AB at C.

What is the ratio $\frac{A C}{B C}$ for the following construction method?

What is the ratio $\frac{A C}{B C}$ for the following construction method:
A line segment AB is drawn.
A single ray is extended from A and 12 arcs of equal lengths are cut, cutting the ray at $A_{1}$ , $A_{2}$ … $A_{12}$ .
A line is drawn from $A_{12}$ to B and a line parallel to $A_{12}$ B is drawn, passing through the point $A_{6}$ and cutting AB at C

Join BYJU'S Learning Program

A line m through A is drawn parallel to BD. A point S moves such that its distances from BD and the vertex A are equal. If the locus of S cuts the line m at T2 and T3, and AC at T1 then ar(△T1T2T3) in square units is

The correct option is C 1Since AG=√2∴AT1=T1G=1√2As A is the focus T1 is the vertex and BD is the directrix of parabolaAlso T2T3 is latusrectum∴T2T3=4.1√2Therefore area T1T2T3=12×1√2×4√2=1

A line m through A is drawn parallel to BD. A point S moves such that its distances from BD and the vertex A are equal. If the locus of S cuts the line m at $T_{2}$ and $T_{3},$ and AC at $T_{1}$ then ar $(△ T_{1} T_{2} T_{3})$ in square units is