MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Multiplication with Vectors

If d1 d...

Question

If $d_{1}$ & $d_{2}$ are the longest and shortest distances of $(- 7, 2)$ from the curve whose equation is $x^{2} + y^{2} - 10 x - 14 y = 51$ then Geometric mean of $d_{1}$ & $d_{2}$ is?

A

\sqrt{11}

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

B

7

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

C

2

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

D

2 \sqrt{11}

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

Open in App

Solution

The correct option is D $2 \sqrt{11}$
$x^{2} + y^{2} - 10 x - 14 y - 51 = 0$ $P (- 7, 2)$
Center $(5, 7)$ Radius = $5 \sqrt{5}$
Longer distance $d_{1} = \sqrt{(7 + 5)^{2} + (7 - 2)^{2}} + 5 \sqrt{5}$
$= 13 + 5 \sqrt{5}$
Short distance $d_{2} = 13 - 5 \sqrt{5}$
$G M = \sqrt{(13 + 5 \sqrt{5}) (13 - 5 \sqrt{5})} = \sqrt{169 - 125}$
$= \sqrt{44}$
$= 2 \sqrt{11}$

Suggest Corrections

thumbs-up

1

Similar questions

d_{1}

d_{2}

are the longest and the shortest distances of the point

P (- 7, 2)

from the circle

x^{2} + y^{2} - 10 x - 14 y - 51 = 0,

then the value of

d_{1}^{2} + d_{2}^{2}

d_{1}, d_{2}

be the longest and shortest distance of a point

P (7, 2)

x^{2} + y^{2} - 10 x - 14 y - 51 = 0.

Then the geometric mean of

d_{1}

d_{2}

p

q

be the longest distance and the shortest distance respectively of the point

(- 7, 2)

(α, β)

on the curve whose equation is

x^{2} + y^{2} - 10 x - 14 y - 51 = 0

p

q

p

q

be the longest distance and the shortest distance respectively of the point

(- 7, 2)

(α, β)

on the curve whose equation is

x^{2} + y^{2} - 10 x - 14 y - 51 = 0

G M

p

q

Q. Question 5
An object is put one by one in three liquids having different densities. The object floats with

\frac{1}{9}

\frac{2}{11}

\frac{3}{7}

parts of their volumes outside the liquidsurface in liquids of densities

d_{1}

d_{2}

d_{3}

respectively. Which of the following statement is correct?

(a)

d_{1}

d_{2}

d_{3}

d_{1}

d_{2}

d_{3}

d_{1}

d_{2}

d_{3}

d_{1}

d_{2}

d_{3}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Basic Operations

PHYSICS

Watch in App

explore_more_icon

Explore more

Multiplication with Vectors

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon