Question

Assertion :The equation of circle having radius √10 and a diameter along line 2x+y=5is x2+y2−6x+2y=0 Reason: 2x+y=5 is a tangent to the circle x2+y2−6x+2y=0.

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Solution

The correct option is **D** Assertion is true ; Reason is false.

Equation of circle given:

Equation of circle given:

⇒x2+y2−6x+2y=0

∴ Centre →(3,−1)→(−g,−f)

(3,−1) satisfies 2x+y=5

(∵2(3)−1=5)

∴2x+y=5 represents diameter

Radius of circle =√g2+f2−c

=√9+1−0

=√10

Hence, assertion is true.

∵2x+y=5 is diameter line , hence it cannot be the tangent to the given circle.

∴ Assertion is true, reason is false.

∴D) Correct.

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