Find the length d of the tangent to the circle x^2+y^2+10 x-6 y-8=0 from the centre of the circle x^2+y^2-4 x=0.

Compute the distance d of the point P(-3,4) from the line 2 x+3 y-6=0.

Find the polar equation of the circle whose cartesian equation is x^2+y^2=4 x.

A thin metal bar \mathrm {AB} of length 10 \mathrm {~cm} leans against a vertical wall. A point P(x, y) moves along the metal bar such that it is 3 \mathrm {~cm} from the end with the horizontal. Find the locus of P.

Evaluate \displaystyle \lim _{x \rightarrow \infty }\left \{\frac {\ln \left [x\left (1+\frac {1}{x}\right )\right ]}{\ln x^2}\right \}.

If the straight line x-y-6=0 intersects the curve y^2=8 x at the points P and Q, calculate |P Q|.

Find the coordinates of the points of intersection of the circles x^2+y^2-6 x-4 y- 13=0 and x^2+y^2-10 x+10 y-15=0.

Which of the choices below represents the slope-intercept form of the equation of a straight line through the points P(a, 0) and Q(0, b)?

The polar equation of a curve is given by r \cos (\theta -\alpha )=\rho , where \theta is the polar angle and \alpha , \rho are constants. Find the cartesian equation of the curve.

Find the equations of the tangents T_1 and T_2 to the curve y=x^3-6 x^2+12x+2 which are parallel to the line y-3x=0.