Let `L_(1)` be a straight line passing through `(0,0) and L_(2)` be x+y=1. If the intercepts made by the circel `x^(2)+y^(2)-x+3y=0on L_(1)and L_(2)` are equal, then which of the following equations can represent `L_(1)`?

Let L_1 be a straight line passing through the origin and L_2 be the straight line x + y = 1 if the intercepts made by the circle x^2 + y^2-x+ 3y = 0 on L_1 and L_2 are equal, then which of the following equations can represent L_1 ?

Let l be the line through (0,0) an tangent to the curve y = x^(3)+x+16. Then the slope of l equal to :

A line L is perpendicular to the line 3x-4y-7=0 and touches the circle x^(2)+y^(2)-2x-4y-4=0 , the y -intercept of the line L can be:

A line L is perpendicular to the line 3x-4y-7=0 and touches the circle x^(2)+y^(2)-2x-4y-4=0 , the y -intercept of the line L can be:

Consider the lines given by L_(1):x+3y-5=0 L_(2):3x-ky-1=0 L_(3):5x+2y-12=0 Match the following lists.

A straight line L through the point (3,-2) is inclined at an angle 60^@ to the line sqrt(3)x+y=1 . If L also intersects the x-axis then find the equation of L .

t_(1),t_(2),t_(3) are lengths of tangents drawn from a point (h,k) to the circles x^(2)+y^(2)=4,x^(2)+y^(2)-4=0andx^(2)+y^(2)-4y=0 respectively further, t_(1)^(4)=t_(2)^(2)" "t_(3)^(2)+16 . Locus of the point (h,k) consist of a straight line L_(1) and a circle C_(1) passing through origin. A circle C_(2) , which is equal to circle C_(1) is drawn touching the line L_(1) and the circle C_(1) externally. Equation of L_(1) is

The combined equation of the lines L_(1) and L_(2) is 2x^(2)+6xy+y^(2)=0 and that lines L_(3) and L_(4) is 4x^(2)+18xy+y^(2)=0 . If the angle between L_(1) and L_(4) be alpha , then the angle between L_(2) and L_(3) will be

If the line l x+m y-1=0 touches the circle x^2+y^2=a^2 , then prove that (l , m) lies on a circle.

If the line l x+m y-1=0 touches the circle x^2+y^2=a^2 , then prove that (l , m) lies on a circle.