Conic Section · Mathematics · NDA

Consider any point P on the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over 9} = 1$$ in the first quadrant. Let r and s represent its distances from (4, 0) and ($$-$$4, 0) respectively, then (r + s) is equal to

The eccentricity of the hyperbola 16x² $$-$$ 9y² = 1 is

What is the equation of the hyperbola having latusrectum and eccentricity 8 and $${3 \over {\sqrt 5 }}$$ respectively?

If the ellipse $$9{x^2} + 16{y^2} = 144$$ intercepts the line $$3x + 4y = 12$$, then what is the length of the chord so formed?

What is the eccentricity of rectangular hyperbola?

What are the coordinates of the point on the parabola which is closest to the straight line?

What is the shortest distance from the above point on the parabola to the line?

A man running round a racecourse notes that the sum of the distances of two flag-posts from him is always 10 m and the distance between the flag-posts is 8 m. The area of the path he encloses is

The position of the point (1, 2) relative to the ellipse 2x² + 7y² = 20 is

The equation of the ellipse whose centre is at origin, major axis is along X-axis with eccentricity $${3 \over 4}$$ and latusrectum 4 units is

What is the equation of the ellipse having foci ($$\pm$$2, 0) and the eccentricity $${1 \over 4}$$ ?

The second degree equation $${x^2} + 4{y^2} - 2x - 4y + 2 = 0$$ represents

What is the equation of the ellipse whose vertices are ($$\pm$$ 5, 0) and foci are at ($$\pm$$ 4, 0) ?

If the angle between the lines joining the end points of minor axis of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ with one of the its foci is $${\pi \over 2}$$, then what is the eccentricity of the ellipse?

The sum of the focal distances of a point on an ellipse is constant and equal to

The equation $$2{x^2} - 3{y^2} - 6 = 0$$ represents

The two parabolas y² = 4ax and x² = 4ay intersect

Consider the following with regard to eccentricity (e) of a conic section:

1. e = 0 for circle

2. e = 1 for parabola

3. e < 1 for ellipse

Which of the above statements is/are correct?