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Diametric Form of a Circle - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Diametric Form of a Circle is considered one the most difficult concept.

  • 8 Questions around this concept.

Solve by difficulty

QuestionMEDIUM

The intercept on the line \mathrm{y=x} by the circle \mathrm{x^{2}+y^{2}-2 x=0} is \mathrm{A B}. The equation of the circle with \mathrm{A B} as a diameter is:

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One of the diameters of the circle circumscribing the rectangle \mathrm{A B C D} is \mathrm{4 y=x+7}. if \mathrm{A} and \mathrm{b} are (-3,4),(5,4), the area of the rectangle is 

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Concepts Covered - 1

Diametric Form of a Circle

Diametric Form of a Circle: 

The equation of circle, when endpoints A (x1, y1) and B(x2, y2) of a diameter are given, is

\mathrm{\left(x-x_{1}\right)\left(x-x_{2}\right)+\left(y-y_{1}\right)\left(y-y_{2}\right)=0}  

Proof:

P(x,y) is any point on the circle

\\ \text { Slope of } \mathrm{AP}=\frac{\mathrm{y}-\mathrm{y}_{1}}{\mathrm{x}-\mathrm{x}_{1}} \\ \text { Slope of } \mathrm{BP}=\frac{\mathrm{y}-\mathrm{y}_{2}}{\mathrm{x}-\mathrm{x}_{2}} \\\because \angle \mathrm{APB}=90^{\circ} \\\therefore \text{Slope of }\mathrm{AP} \times \mathrm{Slope\; of \;}\mathrm{BP}=-1\\ \mathrm{\Rightarrow\left(\frac{y-y_{1}}{x-x_{1}}\right) \times\left(\frac{y-y_{2}}{x-x_{2}}\right)=-1} \\ \mathrm{\Rightarrow\left(x-x_{1}\right)\left(x-x_{2}\right)+\left(y-y_{1}\right)\left(y-y_{2}\right)=0}

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Diametric Form of a Circle

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Diametric Form of a Circle Current Topic

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Circumcentre and Orthocentre
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Area of Triangle in Coordinate Geometry
Locus
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Diametric Form of a Circle

Mathematics for Joint Entrance Examination JEE (Advanced) : Coordinate Geometry

Page No. : 4.9

Line : 5

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