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Statement-1: The line x+9y-12=0 is the ...

Statement-1: The line `x+9y-12=0` is the chord of contact of tangents drawn from a point P to the circle `2x^(2)+2y^(2)-3x+5y-7=0`.
Statement-2: The line segment joining the points of contacts of the tangents drawn from an external point P to a circle is the chord of contact of tangents drawn from P with respect to the given circle

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement-2 is True.

Text Solution

Verified by Experts

The correct Answer is:
D
Statement-2 is the definition of chord of contact of tangents drawn from a point to a given circle. So, it is true.
Let x+9y-12=0 be the chord of contact of tangents drawn from a point p(h, k) to the circle `2x^(2)+2y^(2)-3x+5y-7=0`.
Then its equation is
`hx+ky-(3)/(4)(x+h)+(5)/(4)(y+k)-(7)/(2)=0`
or, `(4h-3)x+(4k+5)y-3h+5k-14=0`
This should be same as `x+9y-12=0`.
`:. (4h-3)/(1)=(4k+5)/(9)=(3h-5k+14)/(12) rArr h=1, k=1`
But, (1,1) lies inside hte circle `2x^(2)+2y^(2)-3x+5y-7=0`.
So, `x+9y-12=0` cannot be the chord of contact of tangents drawn from P. Hence, statement-1 is not true.
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