NCERT Class 11-Math՚S: Exemplar Chapter – 11 Conic Sections Part 10 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 32:

Find the equation of the hyperbola with

(a) Vertices , foci

(b) Vertices

(c) Foci , passing through

Answer:

(a)

(b)

(c)

Objective Type Questions

State whether the statements in each of the Exercises from 33 to 40 are True or False. Justify

Question 33:

The line is a diameter of the circle .

Answer: False

Question 34:

The shortest distance from the point to the circle is equal to .

[Hint: The shortest distance is equal to the difference of the radius and the distance between the centre and the given point.]

Answer: False

Question 35:

If the line is a tangent to the circle , then the point lies on a circle.

[Hint: Use that distance from the centre of the circle to the given line is equal to radius of the circle.]

Answer: True

Question 36:

The point lies inside the circle .

Answer: False

Question 37:

The line will touch the parabola if .

Answer: True

Question 38:

If P is a point on the ellipse whose foci are and , then .

Answer: False

Question 39:

The line touches the ellipse at the point

Answer: True

Question 40:

The locus of the point of intersection of lines and for different value of is a hyperbola whose eccentricity is .

[Hint: Eliminate k between the given equations]

Answer: True

Fill in the Blank in Exercises from 41 to 46

Question 41:

The equation of the circle having centre at and touching the line is ________ .

[Hint: To determine radius find the perpendicular distance from the centre of the circle to the line.]

Answer:

Question 42:

The equation of the circle circumscribing the triangle whose sides are the lines is ________ .

Answer:

Question 43:

An ellipse is described by using an endless string which is passed over two pins. If the axes are and , the length of the string and distance between the pins are ________.

Answer:

Question 44:

The equation of the ellipse having foci , and minor axis of length is ________ .

Answer:

Question 45:

The equation of the parabola having focus at and the directrix is ________.

Answer: