Identify correct statement(s) about conic x - 5 2 + y - 7 2 + x + 1 2 + y + 1 2 = 12

conic is ellipse with major axis 4 x - 3 y + 1 = 0

conic is hyperbola with foci 5 , 7 and - 1 , - 1

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 17

MEDIUM

JEE Main

IMPORTANT

Earn 100

The ratio of the area enclosed by the locus of the midpoint of $P S$ and area of the ellipse is ( $P$ be any point on the ellipse and $S$ is its focus)

31.55% studentsanswered this correctly

Important Questions on Ellipse

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 18

Number of integral values of

α

for which the point

(7 - \frac{5}{4} α, α)

lies inside the ellipse

\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1

is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 19

Coordinates of the vertices

B

and

C

of a triangle

A B C

are

(2, 0)

and

(8, 0)

, respectively. The vertex

A

is varying in such a way that

4 \tan \frac{B}{2} \cdot \tan \frac{C}{2} = 1 .

Then locus of

A

is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 20

P Q

and

Q R

are two focal chords of an ellipse and the eccentric angles of

P, Q

and

R

are

2 α, 2 β

and

2 γ

respectively, then

\tan β \tan γ

is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 21

In triangle $A B C, a = 4$ and $b = c = 2 \sqrt{2}$ . A point $P$ moves within the triangle such that the square of its distance from $B C$ is half the area of rectangle contained by its distances from the other two sides. If $D$ is the centre of locus of $P$ , then