Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Conic Sections>CHAPTER TEST>Q 6

HARD

11th ICSE

IMPORTANT

Earn 100

Show that the equation $5 x^{2} + 30 x + 2 y + 15 = 0$ represents a parabola. find its vertex, focus, length of latus rectum and equations of directrix and axis of parabola?

Important Questions on Conic Sections

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Conic Sections>CHAPTER TEST>Q 7

Find the equation of the parabola with its axis parallel to

y

-axis and passing through the points

(4, 5), (- 2, 11) and (- 4, 21)

.

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Conic Sections>CHAPTER TEST>Q 8

Identify the curve represented by

2 x^{2} - 10 x y + 12 y^{2} + 10 x - 16 y - 3 = 0

?

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Conic Sections>CHAPTER TEST>Q 8

Identify the curve represented by

9 x^{2} - 24 x y + 16 y^{2} - 6 x + 8 y - 5 = 0

?

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Conic Sections>CHAPTER TEST>Q 8

Identify the curve represented by

6 x^{2} - 5 x y - 6 y^{2} + 14 x + 6 y - 4 = 0

?

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Conic Sections>CHAPTER TEST>Q 9

Show that the line

y = x + \sqrt{\frac{5}{6}}

touches the ellipse

3 x^{2} + 2 y^{2} = 1

. Also find the coordinates of the point of contact?

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Conic Sections>CHAPTER TEST>Q 10

Determine

k

so that the line

2 x + y + k = 0

may touch the hyperbola

3 x^{2} - y^{2} = 3

?

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Conic Sections>CHAPTER TEST>Q 11

Find the equations of tangents to the ellipse

4 x^{2} + 5 y^{2} = 20

which are perpendicular to the line

3 x + 2 y - 5 = 0

.