NCERT Exemplar Mathematics - Class 11>Chapter 11 - Conic Sections>EXERCISE>Q 43

HARD

11th CBSE

IMPORTANT

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An ellipse is described by using an endless string which is passed over two pins. If the axes are $6 cm$ and $4 cm,$ then length of the string and distance between the pins are $a + 2 \sqrt{5}$ cm and $b \sqrt{5}$ cm, then $a + b =$

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Important Questions on Conic Sections

HARD

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 11 - Conic Sections>EXERCISE>Q 44

The equation of the ellipse having foci

(0, 1), (0, - 1)

and minor axis of length

1

is

\frac{x^{2}}{k} + \frac{y^{2}}{\frac{5}{4}} = 1

, then

k =

_____

HARD

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 11 - Conic Sections>EXERCISE>Q 45

The equation of the parabola having focus at

(- 1, - 2)

and the directrix is

x - 2 y + 3 = 0

is

m x^{2} + y^{2} + 4 x y + 4 x + 32 y + n = 0, m + n =

_____.

HARD

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 11 - Conic Sections>EXERCISE>Q 46

The equation of the hyperbola with vertices at

(0, \pm 6)

and having eccentricity

\frac{5}{3}

is

\frac{y^{2}}{36} - \frac{x^{2}}{k^{2}} = 1

then positive value of

k =

_____

MEDIUM

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 11 - Conic Sections>EXERCISE>Q 47

The area of the circle (in sq. units) centered at

(1, 2)

and passing through

(4, 6)

is

HARD

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 11 - Conic Sections>EXERCISE>Q 48

Equation of a circle which passes through

(3, 6)

and touches the axes is

HARD

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 11 - Conic Sections>EXERCISE>Q 49

Equation of the circle with center on the

y

-axis and passing through the origin and the point

(2, 3)

is

HARD

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 11 - Conic Sections>EXERCISE>Q 50

The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length

3 a

is

HARD

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 11 - Conic Sections>EXERCISE>Q 51

If the focus of a parabola is

(0, - 3)

and its directrix is

y = 3

then its equation is