Question

If the point (1, 4) lies inside the circle x2 + y2 – 6x – 10y + p = 0 and the circle does not touch or interest the coordinates axes, then

Solution

Correct option is

25 < p < 29

Since the circle does not touch or intersect the coordinates axes, the absolute values of x and y coordinates of the centre are greater than the radius of the circle. Coordinates of the centre of the circle are (3, 5) and the radius is   

             

and the point (1, 4) lies inside the circle

  

From (1), (2), (3) we get  

                               25 < p < 29.

SIMILAR QUESTIONS

Q1

If a line segment AM = a moves in the plane XOY remaining parallel toOX so that the left end point A slides along the circle x2 + y2 = a2, the locus of M is

Q2

If common chord of the circle C with centre at (2, 1) and radius r and the circle x2 + y2 – 2x – 6y + 6 = 0 is a diameter of the second circle, then the value of r is  

Q3

Tangents drawn from the point P(1, 8) to the circle x2 + y2 – 6x – 4y – 11 = 0 touch the circle at the points A and B. The equation of the circumcircle of the triangle in PAB is

Q4

Let ABCD be a quadrilateral with area 18, with side AB parallel to CD and AB = 2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is

Q5

An equilateral triangle is inscribed in the circle x2 + y2 = a2 with the vertex at (a, 0). The equation of the side opposite to this vertex is

Q6

The lines 2x – 3y = 5 and 3x – 4y = 7 are the diameters of a circle of area 154 square units. An equation of this circle is (π = 22/7)

Q7

The equation f a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is

Q8

A line is drawn through the point P(3, 11) to cut the circle x2 + y2 = 9 at A and B. Then PAPB is equal to

Q9

Two rods of lengths a and b slide along the x-axid and y-axis respectively in such a manner that their ends are concyclic. The locus of the centre of the circle passing through the end points is

Q10

If the line x cos α + y sin α = p represents the common chord APQB of the circle x2 + y2 = a2 and x2 + y2 = b2 (a > b) as shown in the Fig, then AP is equal to