Find the equations of tangents and normal for the circle: x² + y² = 5 at (1,2).

Find the equations of tangent and normal for the circle: x² + y² = 25 at (3,4).

Find the equation of tangent and normal to the circle: x² + y² = 100 at (1,2).

Find the equation of tangent and normal to the circle: x² + y² = 169 at (12,-5).

Find the equation of tangent and normal to circle: x² + y² - 2x - 4y + 3 = 0 at (2,3).

Find the equation of tangent and normal to the circle: x² + y² - 3x + 4y - 31 = 0 at (-2,3).

Find the length of the intercept made by the straight line x + y = 3 with the circle x² + y² - 2x - 3 = 0.

Find the length of the intercepts made by the straight line 2x - y = 7 with the circle x² + y² - 6x - 8y + 15 = 0.

Write the condition for a line y = mx + c to be tangent to the circle x² + y² = a².

Show that the line 3x + 4y - 20 = 0 touches the circle x² + y² = 16. Also, find the point of contact.

Show that the line 3x - 4y = 25 and the circle x² + y² = 25 intersect at a coincident point.

Define tangent and normal to a circle.

Find the equation of the tangent to the circle x² + y² = 25 inclined at an angle of 60^o to the x-axis.

Find the equation of the tangent to the circle x² + y² = 9 parallel to 3x + 4y = 0.

Find the equation of the tangent to the circle x² + y² -6x + 4y = 12 and parallel to the line 4x + 3y + 5 = 0.

Find the equation of the tangents to the circle x² + y² = 5, which are perpendicular to the line x + 2y = 0.

Find the equation of the tangents to the circle x² + y² - 2x - 4y -4 = 0 which are perpendicular to the line 3x - 4y = 1.

Find the equation of the tangent to the circle x² + y² = 10 at the point whose abscissa is 1.

Find the equation of the tangent to the circle x + y - 2ax = 0 at $\rm (a (1 + \cos \alpha ), a \sin \alpha)$.

Find the value of k if the line 2x - y + k = 0 may touch the circle x² + y² = 5.

The equation of tangent (3, 4) to the circle x² + y² = 25 is