NCERT Class 11-Math՚S: Exemplar Chapter – 11 Conic Sections Part 9 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Long Answer Type

Question 23:

If the lines and are the diameters of a circle of area square units, then obtain the equation of the circle.

Answer:

Question 24:

Find the equation of the circle which passes through the points and and the centre lies on the straight line .

Answer:

Question 25:

Find the equation of a circle whose centre is and which cuts off a chord of length 6 units on the line .

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

Answer:

Question 26:

Find the equation of a circle of radius which is touching another circle at (5,5) .

Answer:

Question 27:

Find the equation of a circle passing through the point having radius units and whose centre lies on the line .

Answer:

Question 28:

Find the equation of each of the following parabolas

(a) Directrix , focus at

(b) Vertex at , focus at

(c) Focus at , directrix

Answer:

(a)

(b)

(c)

Question 29:

Find the equation of the set of all points the sum of whose distances from the points and is .

Answer:

Question 30:

Find the equation of the set of all points whose distance from are of their distance from the line .

Answer:

Question 31:

Show that the set of all points such that the difference of their distances from and is always equal to represent a hyperbola.

Answer:

Let the point be

As per the question,

Distance of from - Distance of from

Distance between the points [Distance Formula]

Squaring both the sides,

Squaring both the sides,

Hence, the required equation is , which is a parabola.