NCERT Solutions
Class 11 - Mathematics - Chapter 10: CONIC SECTIONS
EXERCISE 10.1

Open NCERT PDFOpen NCERT Answers PDF

Question. 1

Find the equation of the circle with centre \((0,2)\) and radius 2.

Answer:

x^2 + y^2 - 4y = 0

Question. 2

Find the equation of the circle with centre \((-2,3)\) and radius 4.

Answer:

x^2 + y^2 + 4x - 6y - 3 = 0

Question. 3

Find the equation of the circle with centre \(\left(\dfrac{1}{2}, \dfrac{1}{4}\right)\) and radius \(\dfrac{1}{12}\).

Answer:

36x^2 + 36y^2 - 36x - 18y + 11 = 0

Question. 4

Find the equation of the circle with centre \((1,1)\) and radius \(\sqrt{2}\).

Answer:

x^2 + y^2 - 2x - 2y = 0

Question. 5

Find the equation of the circle with centre \((-a,-b)\) and radius \(\sqrt{a^2 - b^2}\).

Answer:

x^2 + y^2 + 2ax + 2by + 2b^2 = 0

Question. 6

Find the centre and radius of the circle \((x+5)^2 + (y-3)^2 = 36\).

Answer:

c(-5, 3), r = 6

Question. 7

Find the centre and radius of the circle \(x^2 + y^2 - 4x - 8y - 45 = 0\).

Answer:

c(2, 4), r = \(\sqrt{65}\)

Question. 8

Find the centre and radius of the circle \(x^2 + y^2 - 8x + 10y - 12 = 0\).

Answer:

c(4, -5), r = \(\sqrt{53}\)

Question. 9

Find the centre and radius of the circle \(2x^2 + 2y^2 - x = 0\).

Answer:

c\(\left(\dfrac{1}{4}, 0\right)\), r = \(\dfrac{1}{4}\)

Question. 10

Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre lies on the line \(4x + y = 16\).

Answer:

x^2 + y^2 - 6x - 8y + 15 = 0

Question. 11

Find the equation of the circle passing through the points (2,3) and (−1,1) and whose centre is on the line \(x - 3y - 11 = 0\).

Answer:

x^2 + y^2 - 7x + 5y - 14 = 0

Question. 12

Find the equation of the circle with radius 5 whose centre lies on the x-axis and passes through the point (2,3).

Answer:

x^2 + y^2 + 4x - 21 = 0 and x^2 + y^2 - 12x + 11 = 0

Question. 13

Find the equation of the circle passing through (0,0) and making intercepts \(a\) and \(b\) on the coordinate axes.

Answer:

x^2 + y^2 - ax - by = 0

Question. 14

Find the equation of the circle with centre (2,2) and passing through the point (4,5).

Answer:

x^2 + y^2 - 4x - 4y = 5

Question. 15

Does the point \((-2.5, 3.5)\) lie inside, outside or on the circle \(x^2 + y^2 = 25\)?

Answer:

Inside the circle; since the distance of the point to the centre of the circle is less than the radius of the circle.