Interaction between Circle and a Line

IMPORTANT

Interaction between Circle and a Line: Overview

This topic covers concepts, such as Interaction between Line and a Circle, Position of a line with respect to a circle, Condition For Tangency to a Circle, Chord of a Circle, Length of the Chord of a Circle, Image of a Circle in a Line Mirror, etc.

Important Questions on Interaction between Circle and a Line

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IMPORTANT

Find the point on the straight line, y = 2x + 11 which is nearest to the circle,  1 6 x 2 + y 2 + 3 2 x - 8 y - 5 0 = 0

HARD
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One of the diameters of the circle circumscribing the rectangle ABCD is 4y=x+7. If A and B are the points - 3,4 and 5, 4, respectively, then the area of the rectangle is 

HARD
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All the chords of the curve   3 x 2 y 2 2x+4y=0,  which subtend a right angle at the origin, pass through a fixed point. Find the coordinates of the point.

EASY
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The points of intersection of the line   4x3y10=0 and the circle  x2+y22x+4y20=0 are:

HARD
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7y-x-5=0 touches the circle x2+y2-5x+5y=0. The equation of other parallel tangent is

EASY
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The point where the line x+y=5 touches the circle x2+y2-2x-4y+3=0.

HARD
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If m1,m2 are the slopes of the tangents drawn from a point 1,-3 to the circle x2+y2-6x+4y+12=0 then 9m12+m22=

EASY
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The length of the intercept on the line 4x-3y-10=0 by the circle x2+y2-2x+4y-20=0 is

EASY
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The points of intersection of the line y=x+2 and the circle x-22+y2=16 are

HARD
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Let C be a circle passing through the points A2,-1 and B3,4. The line segment AB is not a diameter of C. If r is the radius of C and its centre lies on the circle x-52+y-12=132, then r2 is equal to:

MEDIUM
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In the given figure, ABCD is a cyclic quadrilateral such that ADB=50° and DCA=70°, then find the measure of DAB.

Question Image

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The radius of a circle whose center lies in the fourth quadrant and touches each of the three lines x=0, y=0 and 3x+4y-12=0, is ............ units.

MEDIUM
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The length of the chord intercepted by the circle x2+y2-8x-2y-8=0 on the line x+y+1=0 is ______ units.

EASY
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If the parametric values of two points A,B on the circle x2+y2-6x+4y-12=0 are 30° and 90°, respectively, then the equation of chord AB¯ is _______

MEDIUM
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Equation of the circle, which is the mirror image of the circle x2+y2-2x=0 with respect to the line x+y=2, is

MEDIUM
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If one of the diameters of the circle x2+y2-2x-6y+6=0 is a chord to the circle with centre 2, 1, then the radius of the circle is

MEDIUM
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The circle x2+y2-3x-4y+2=0 cuts x-axis at

MEDIUM
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The locus of centre of a circle which passes through the origin and cuts off a length of 4 unit from the line x=3 is

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Radius of circle in which a chord length 2 makes an angle π2 at the centre, is

EASY
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If a chord of circle of radius 12 unit is trisected at points 2,9 & 1,2, then the distance of the chord from centre is