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Different Form of the Equation of the Circle is considered one the most difficult concept.
34 Questions around this concept.
The centres of those circles which touch the circle, x2+y2−8x−8y−4=0, externally and also touch the x-axis, lie on :
The circle passing through (1,-2) and touching the axis of x at (3,0) also passes through the point :
Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and touching the circle C externally, then the radius of T is equal to :
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A circle touches the lines the centre of this circle lies in the first quadrant then one possible equation of this circle is
Equation of circle touching the lines will be
Four distinct points lie on a circle when:
Intercepts Made by Circle on the Axis
If the equation of Circle is , then
Length of x-intercept :
Length of y-intercept :
Proof:
Different Form of a Circle
When the circle touches X-axis
(a,b) be the centre of the circle, then radius = |b|
When the circle touches Y-axis
(a,b) be the centre of the circle, then radius = |a|
When the circle touches both the axes:
(a,a) be the centre of the circle, then radius = |a|
Note:
In this case, the centre can also be (a, -a) and radius |a|.
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Mathematics for Joint Entrance Examination JEE (Advanced) : Coordinate Geometry
Page No. : 4.4
Line : 37
July 04, 2019
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