Given the circle C with the equation x² + y² - 2x + 10y - 38 = 0. Match the List I with the List II given below concerning C

	List I		List II
A	The equation of the polar of (4, 3)with respect to C	I	y + 5 = 0
B	The equation of the tangent at (9, - 5) on C	II	x = 1
C	The equation of  the normal at(- 7, - 5) on C	III	3x + 8y = 27
D	The equation of the diameter of  C passing through (1,3)	IV	x + y = 3
		V	x = 9

The correct answer is

The equation of a straight line passing through the point (1, 2) and inclined at 45° to the line y = x + 1 is

• 5x + y = 7

• 3x + y = 5

• x + y = 3

• x - y + 1 = 0

$$\begin{gathered} \mathrm{The} \mathrm{distance} \mathrm{between} \mathrm{the} \mathrm{parallel} \mathrm{lines} \mathrm{given} \mathrm{by} \\ {\left(\mathrm{x} + 7\mathrm{y}\right)}^2 + 4\sqrt{2}\left(\mathrm{x} +\hspace{0.17em}7\mathrm{y}\right) - 42 = 0 \mathrm{is} \end{gathered}$$

• $\frac{4}{5}$

• $4\sqrt{2}$

• 2

• $10\sqrt{2}$

4.

If the area of the triangle formed by the pair of lines 8x² - 6xy + y² = 0 and the line 2x + 3y = a is 7, then a is equal to

• 14

• $14\sqrt{2}$

• $28\sqrt{2}$

• 28

If the line x + 3y = 0 is the tangent at (0, 0) to the circle of radius 1, then the centre of one such circle is

• (3, 0)

• $\left(\frac{- 1}{\sqrt{10}}, \frac{3}{\sqrt{10}}\right)$

• $\left(\frac{3}{\sqrt{10}}, \frac{- 3}{\sqrt{10}}\right)$

• $\left(\frac{1}{\sqrt{10}}, \frac{3}{\sqrt{10}}\right)$

A circle passes through the point (3, 4) and cuts the circle x² + y² = a² orthogonally; the locus of its centre is a straight line. If the distance of this straight line from the origin is 25, then a is equal to

• 250

• 225

• 100

• 25

The equation to the line joining the centres of the circles belonging to the coaxial system of circles 4x² + 4y² - 12x + 6y - 3 + $\mathrm{\lambda }$(x + 2y - 6) = 0 is

• 8x - 4y - 15 = 0

• 8x - 4y + 15 = 0

• 3x - 4y - 5 = 0

• 3x - 4y + 5 = 0

Let x + y = k be a normal to the parabola y² = 12x. If p is length of the perpendicular from the focus of the parabola onto this normal, then 4k - 2p² is equal to

• 1

• 0

• - 1

• 2

If the line 2x + 5y = 12 intersects the ellipse 4x² + 5y² = 20 in two distinct points A and B,then mid-point of AB is

• (0, 1)

• (1, 2)

• (1, 0)

• (2, 1)

Equation of one of the tangents passing through(2, 8) to the hyperbola 5x² - y² = 5 is

• 3x + y - 14 = 0

• 3x - y + 2 = 0

• x + y + 3 = 0

• x - y + 6 = 0