Definition of a circle

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Question

$The square of diameter of the circle having tangent at (1, 1) as x + y - 2 = 0 and passing through (2, 2) is ……$

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Solution

$Given equation of tangent at P (1, 1) is x + y - 2 = 0$
$Then, normal equation at P is x - y = 0$
$\Rightarrow Diameter will be x - y = 0$
$And Q (2, 2) lies on x - y = 0$
$\Rightarrow It is other end of diameter$
$∴ Length of diameter = P Q = \sqrt{1 + 1} = \sqrt{2}$
Square of the length of the diameter = 2
Therefore, the correct answer is 2.00

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Definition of a circle

Remember concepts with our Masterclasses.

The square of diameter of the circle having tangent at (1,1) as x+y−2=0 and passing through (2, 2) is ……

Given equation of tangent at P(1,1) is x+y−2=0 Then, normal equation at P is x−y=0⇒ Diameter will be x−y=0 And Q(2,2) lies on x−y=0⇒ It is other end of diameter ∴ Length of diameter =PQ=1+1=2 Square of the length of the diameter = 2 Therefore, the correct answer is 2.00

Ready to Test Your Skills?

free study material

$The square of diameter of the circle having tangent at (1, 1) as x + y - 2 = 0 and passing through (2, 2) is ……$