OP Malhotra Class-11 Circle S.Chand ISC Maths Solution Chapter-17. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-17 (a), 17 (b), 17 (c), 17 (d), With Chapter Test. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.
OP Malhotra Class-11 Circle S.Chand ISC Maths Solution
Class: | 11th |
Subject: | Mathematics |
Chapter : | Ch-17 Circle of Section -A |
Board | ISC |
Writer | OP Malhotra |
Publications | S.Chand Publications 2020-21 |
-: Select Topics :-
OP Malhotra Class-11 Circle S.Chand ISC Maths Solution
Circle
A circle is the set of all points in a plane, which are at a fixed distance from a fixed point in the plane. The fixed point is called the centre of the circle and the distance from centre to any point on the circle is called the radius of the circle.
The equation of a circle with radius r having centre (h, k) is given by (x – h)2 + (y – k)2 = r2.
The general equation of the circle is given by x2 + y2 + 2gx + 2fy + c = 0 , where, g, f and c are constants.
- The centre of the circle is (-g, -f).
- The radius of the circle is r = √𝑔2+𝑓2−𝑐
The general equation of the circle passing through origin is x2 + y2 + 2gx + 2fy = 0.
The parametric equation of the circle x2 + y2 = r2 are given by x = r cos θ, y = r sin θ, where θ is the parametre and the parametric equation of the circle (x – h)2 + (y – k)2 = r2 are given by x = h + r cos θ, y = k + r sin θ.
Note: The general equation of the circle involves three constants which implies that at least three conditions are required to determine a circle uniquely.
Parabola
A parabola is the set of points P whose distances from a fixed point F in the plane are equal to their distance from a fixed line l in the plane. The fixed point F is called focus and the fixed line l is the directrix of the parabola.
Ellipse
An ellipse is the set of all points in a plane such that the sum of whose distances from two fixed points is constant.
Hyperbola
A hyperbola is the locus of a point in a plane which moves in such a way that the ratio of its distance from a fixed point in the same plane to its distance from a fixed line is always constant which is always greater than unity. The fixed point is called the focus, the fixed line is called the directrix and the constant ratio, generally denoted bye, is known as the eccentricity of the hyperbola.
Exe-17 (a)
OP Malhotra Class-11 Circle S.Chand ISC Maths Solution
Page 17-3
Question 1:
Find the equation of the circle.
(i)……………
……………..
Question 2:
…………………….
……………………..
……………………….
Question 10:
The point diametrically …………………… (d) (3, 4)
Exe-17 (b)
OP Malhotra Class-11 Circle S.Chand ISC Maths Solution
Page 17-6 to 17-7
Question 1:
Find the centre and radius of the circle
(i)…………
(ii)…………..
Question 2:
Find the length of ………….. coordinate axis.
Question 3:
……………………
……………………..
…………………….
Question 21:
Find the equation of circle ………….. x + y – 3 = 0
Exe-17 (c)
OP Malhotra Class-11 Circle S.Chand ISC Maths Solution
Page 17-13 to 17-14
Question 1:
The circle ………… the coordinate of A and B.
Question 2:
Find the length of ……………. chord as diameter.
Question 3:
……………………
…………………..
………………….
Question 19:
(i) Prove that the line …………….. point of contact.
(ii) The circle ……………. possible value of p.
Exe-17 (d)
OP Malhotra Class-11 Circle S.Chand ISC Maths Solution
Page 17-16
Question 1:
Find the equation of …………………. perpendicular of y = 2x
Question 2:
Find the equation ………………….. 5x – 2y = 2.
Question 3:
…………………..
……………………
…………………..
Question 7:
Find the focus of the middle …………… drawn through the origin.
Chapter Test
OP Malhotra Class-11 Circle S.Chand ISC Maths Solution
Page 17-17 to 17-18
Question 1:
Find the centre and radius of circle ……….. = 0
Question 2:
………………………..
………………………..
………………………..
…………………………
Question 11:
Find the equation of the circle which ………………………………. from the x-axis.\
-: End of Circle Solution :-
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