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Given, x^2+y^2=1. Y' and y'' are first a...

Given, `x^2+y^2=1`. Y' and y'' are first and second order derivative of y respectively.
Statement-I `1+yy''+(y')^2=0`
Statement- II `x x'+2y=0`

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 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.

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Given, y=tan^-1sqrt(x^2-1), if y_1 and y_2 are the first and second derivatives of y, then prove that x(x^2-1)y_2+(2x^2-1)y_1=0 .

Statement 1 : The equations of the straight lines joining the origin to the points of intersection of x^2+y^2-4x-2y=4 and x^2+y^2-2x-4y-4=0 is x-y=0 Statement 2 : y+x=0 is the common chord of x^2+y^2-4x-2y=4 and x^2+y^2-2x-4y-4=0 (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1. (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

Knowledge Check

  • Statement - I : (x + 2)^(2) + (y-3)^(2) = -1 , this equation cannot represent the equation of a circle. Statement - II : (x+2)^(2) + (y-3)^(2) = -1 cannot represent a real equation of a locus

    A
    Statement- I is true, Statement - II is true and Statement- II is a correct explanation for Statement - I.
    B
    Statement- I is true, Statement - II is true but Statement- II is not a correct explanation for Statement - I.
    C
    Statement- I is true, Statement-II is false.
    D
    Statement- I is false, Statement-II is true.

  • The circle x^2+y^2+x+y=0 and x^2+y^2+x-y=0 intersect at an angle of :

    A
    `pi/6`
    B
    `pi/4`
    C
    `pi/3`
    D
    `pi/2`

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    Statement 1 : The least and greatest distances of the point P(10 ,7) from the circle x^2+y^2-4x-2y-20=0 are 6 units and 15 units, respectively. Statement 2 : A point (x_1,y_1) lies outside the circle S=x^2+y^2+2gx+2fy+c=0 if S_1>0, where S_1=x_1^2+y_1^2+2gx_1+2fy_1+c (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1. (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

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