Consider the hyperbola `H: x^(2)-y^(2)=1` and a circle S with centre `N(x_(2),0)`. Suppose that H ans S touch each other at a point `P(x_(1),y_(1))` with `x_(1)gt1` and `y_(1)gt0`. The common tangent to H ans S at P intersects the x-axis at point M. If (l, m) is the centroid of the triangle PMN, then the correct expression(s) is (are)-

Consider the hyperbola H : x^2-y^2=1 and a circle S with center N(x_2,0) . Suppose that Ha n dS touch each other at a point P(x_1, y_1) with x_1>1 and y_1> 0. The common tangent to Ha n dS at P intersects the x-axis at point Mdot If (l ,m) is the centroid of the triangle P M N , then the correct expression(s) is (are) (d l)/(dx_1)=1-1/(3x1 2)forx_1>1 (d m)/(dx_1)=(x_1)/(3sqrt(x1 2-1)) for x_1> (d l)/(dx_1)=1+1/(3x1 2) for x_1>1 (d m)/(dy_1)=1/3 for x_1>0

Consider the hyperbola H:x^2-y^2=1 and a circile S with center N(x_2,0) . Suppose that H and S touch each other at a point P(x_1,y_1) with x_1gt1andy_1gt0 . The common langent to H and S intersects the x-axis at point M. If (l,m) is the centroid of the triangle trianglePMN , then the correct expression(s)is(are)

Consider the hyperbola H:x^2-y^2=1 and a circle S with centre N(x_2,0) Suppose that H and S touch each other at a point (P(x_1,y_1) with x_1 > 1 and y_1 > 0 The common tangent to H and S at P intersects the x-axis at point M. If (l,m) is the centroid of the triangle DeltaPMN then the correct expression is (A) (dl)/(dx_1)=1-1/(3x_1^2) for x_1 > 1 (B) (dm)/(dx_1) =x_!/(3(sqrtx_1^2-1))) for x_1 > 1 (C) (dl)/(dx_1)=1+1/(3x_1^2) for x_1 > 1 (D) (dm)/(dy_1)=1/3 for y_1 > 0

Consider the hyperbola H:x^2-y^2=1 and a circle S with centre N(x_2,0) Suppose that H and S touch each other at a point (P(x_1,y_1) with x_1 > 1 and y_1 > 0 The common tangent to H and S at P intersects the x-axis at point M. If (l,m) is the centroid of the triangle DeltaPMN then the correct expression is (A) (dl)/(dx_1)=1-1/(3x_1^2) for x_1 > 1 (B) (dm)/(dx_1) =x_!/(3(sqrtx_1^2-1))) for x_1 > 1 (C) (dl)/(dx_1)=1+1/(3x_1^2) for x_1 > 1 (D) (dm)/(dy_1)=1/3 for y_1 > 0

Consider the hyperbola H:x^2-y^2=1 and a circle S with centre N(x_2,0) Suppose that H and S touch each other at a point (P(x_1,y_1) with x_1 > 1 and y_1 > 0 The common tangent to H and S at P intersects the x-axis at point M. If (l,m) is the centroid of the triangle DeltaPMN then the correct expression is (A) (dl)/(dx_1)=1-1/(3x_1^2) for x_1 > 1 (B) (dm)/(dx_1) =x_!/(3(sqrtx_1^2-1))) for x_1 > 1 (C) (dl)/(dx_1)=1+1/(3x_1^2) for x_1 > 1 (D) (dm)/(dy_1)=1/3 for y_1 > 0

The equation of chord with mid-point P(x_(1),y_(1)) to the circle S=0 is

The equation of pair of tangents drawn from an external point P(x_(1),y_(1)) to circle S=0 is

Let the line y = mx intersects the curve y^2 = x at P and tangent to y^2 = x at P intersects x-axis at Q. If area ( triangle OPQ) = 4, find m (m gt 0) .

Let the line y = mx intersects the curve y^2 = x at P and tangent to y^2 = x at P intersects x-axis at Q. If area ( triangle OPQ) = 4, find m (m gt 0) .

Let the line y = mx intersects the curve y^2 = x at P and tangent to y^2 = x at P intersects x-axis at Q. If area ( triangle OPQ) = 4, find m (m gt 0) .