Condition for Orthogonality

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JEE Main 2005

If a circle passes through the point $(a, b)$ and cuts the circle $x^{2} + y^{2} = p^{2}$ orthogonally, then the equation of the locus of its centre is

x^{2} + y^{2} - 3 a x - 4 b y + (a^{2} + b^{2} - p^{2}) = 0

(B)

2 a x + 2 b y - (a^{2} + b^{2} + p^{2}) = 0

(C)

x^{2} + y^{2} - 2 a x - 3 b y + (a^{2} - b^{2} - p^{2}) = 0

(D)

2 a x + 2 b y - (a^{2} + b^{2} + p^{2}) = 0

JEE Main 2004

LEVELJEE Main

If a circle passes through the point $(a, b)$ and cuts the circle $x^{2} + y^{2} = 4$ orthogonally, then the locus of its centre is

(A)

2 a x - 2 b y - (a^{2} + b^{2} + 4) = 0

(B)

2 a x + 2 b y - (a^{2} + b^{2} + 4) = 0

(C)

2 a x - 2 b y + (a^{2} + b^{2} + 4) = 0

(D)

2 a x + 2 b y + (a^{2} + b^{2} + 4) = 0

JEE Advanced 2014

LEVELJEE Main

A circle $S$ passes through the point $(0, 1)$ and is orthogonal to the circles $(x - 1)^{2} + y^{2} = 16$ and $x^{2} + y^{2} = 1$ . Then

* Multiple Correct Options

(A)

radius of

S

is 8

(B)

radius of

S

is 7

(C)

centre of

S

(- 7, 1)

(D)

centre of

S

(- 8, 1)

LEVELBoard

If the circles $x^{2} + y^{2} + 2 x + 2 k y + 6 = 0, x^{2} + y^{2} + 2 k y + k = 0$ intersect orthogonally, then $k$ is

(A)

2

- \frac{3}{2}

(B)

- 2

- \frac{3}{2}

(C)

2

\frac{3}{2}

(D)

- 2

\frac{3}{2}

LEVELJEE Main

If a circle passes through the point $(a, b)$ and cuts the circle $x^{2} + y^{2} = k^{2}$ orthogonally, then the equation of the locus of its centre is

(A)

2 a x + 2 b y - (a^{2} + b^{2} + k^{2}) = 0

(B)

2 a x + 2 b y - (a^{2} - b^{2} + k^{2}) = 0

(C)

x^{2} + y^{2} - 3 a x - 4 b y + (a^{2} + b^{2} - k^{2}) = 0

(D)

x^{2} + y^{2} - 2 a x - 3 b y + (a^{2} - b^{2} - k^{2}) = 0

JEE Advanced 2004

LEVELJEE Advanced

Find the equation of circle touching the line $2 x + 3 y + 1 = 0$ at $(1, - 1)$ and cutting orthogonally the circle having line segment joining $(0, 3)$ and $(- 2, - 1)$ as diameter.

JEE Main 2019 (12 April Shift 1)

LEVELJEE Main

If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90°, then the length (in cm) of their common chord is :

(A)

60/13

(B)

120/13

(C)

13/2

(D)

13/5

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If a circle passes through the point (a,b) and cuts the circle x2+y2=p2 orthogonally, then the equation of the locus of its centre is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If a circle passes through the point (a,b) and cuts the circle x2+y2=4 orthogonally, then the locus of its centre is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A circle S passes through the point (0,1) and is orthogonal to the circles (x−1)2+y2=16 and x2+y2=1. Then

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the circles x2+y2+2x+2ky+6=0,x2+y2+2ky+k=0 intersect orthogonally, then k is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If a circle passes through the point (a,b) and cuts the circle x2+y2=k2 orthogonally, then the equation of the locus of its centre is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Find the equation of circle touching the line 2x+3y+1=0 at (1,−1) and cutting orthogonally the circle having line segment joining (0,3) and (−2,−1) as diameter.

If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90°, then the length (in cm) of their common chord is :

If a circle passes through the point $(a, b)$ and cuts the circle $x^{2} + y^{2} = p^{2}$ orthogonally, then the equation of the locus of its centre is

If a circle passes through the point $(a, b)$ and cuts the circle $x^{2} + y^{2} = 4$ orthogonally, then the locus of its centre is

A circle $S$ passes through the point $(0, 1)$ and is orthogonal to the circles $(x - 1)^{2} + y^{2} = 16$ and $x^{2} + y^{2} = 1$ . Then

If the circles $x^{2} + y^{2} + 2 x + 2 k y + 6 = 0, x^{2} + y^{2} + 2 k y + k = 0$ intersect orthogonally, then $k$ is

If a circle passes through the point $(a, b)$ and cuts the circle $x^{2} + y^{2} = k^{2}$ orthogonally, then the equation of the locus of its centre is

Find the equation of circle touching the line $2 x + 3 y + 1 = 0$ at $(1, - 1)$ and cutting orthogonally the circle having line segment joining $(0, 3)$ and $(- 2, - 1)$ as diameter.