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Tangents are drawn from the point (17, 7...

Tangents are drawn from the point (17, 7) to the circle `x^2+y^2=169`, Statement I The tangents are mutually perpendicular Statement, lls The locus of the points frorn which mutually perpendicular tangents can be drawn to the given circle is `x^2 +y^2=338` (a) Statement I is correct, Statement II is correct; Statement II is a correct explanation for Statementl (b( Statement I is correct, Statement I| is correct Statement II is not a correct explanation for Statementl (c)Statement I is correct, Statement II is incorrect (d) Statement I is incorrect, Statement II is correct

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:
A
The locus of the points from which mutually perpendicular tangents can be drawn to the circle `x^(2)+y^(2)=a^(2)` is the circle `x^(2)+y^(2)=2a^(2)`. The circle `x^(2)+y^(2)=2a^(2)` is known as the director circle of `x^(2)+y^(2)=a^(2)`. Thus, if tangents are drawn from any point on the direction circle to the given circle, then the tangents are mutually perpendicular. Hence statement-1 and 2 are true and statement-2 is a correct explanation for statement-1.
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Tangents are drawn from the point (17, 7) to the circle x^(2)+y^(2)=169 . STATEMENT-1 : The tangents are mutually perpendicular. because STATEMENT-2 : The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x^(2)+y^(2)=338 .

Tangents are drawn from the point (17,7) to the circle x^(2)+y^(2)=169 . STATEMENT-1 : The tangents are mutually perpendicular. because STATEMENT-2 : The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x^(2)+y^(2)=338 .

Knowledge Check

  • Locus of a point from which perpendicular tangents can be drawn to the circle x^(2)+y^(2)=a^(2) is

    A
    circle throụgh origin
    B
    circle of radius 2a
    C
    concentric circle of radius `asqrt(2)`
    D
    none

  • Let F(x) be an indefinite integral of sin^(2)x Statement I The function F(x) satisfies F(x+pi)=F(x) for all real x. Because Statement II sin^(2)(x+pi)=sin^(2)x, for all real x. (A) Statement I is true, Statement II is also true, Statement II is the correct explanation of Statement I. (B)Statement I is true, Statement II is also true, Statement II is not the correct explanation of Statement I. (C) Statement I is true, Statement II is false. (D) Statement I is false, Statement II is ture.

    A
    Statement I is true, Statement II is also true,
    Statement II is the correct explanation of Statement I.
    B
    Statement I is true, Statement II is also true,
    Statement II is not the correct explanation of Statement I.
    C
    Statement I is true, Statement II is false.
    D
    Statement I is false, Statement II is ture.

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