Normal to a Circle

IMPORTANT

Normal to a Circle: Overview

This topic covers concepts, such as, Normal to a Circle & Parametric Form of Normal to a Circle etc.

Important Questions on Normal to a Circle

MEDIUM
IMPORTANT

The line ax+by+c=0 is normal to the circle x2+y2+2gx+2fy+d=0 if _________

HARD
IMPORTANT

Find the slope of the focal chords of the parabola y2=32x, which are tangents to the circle x2+y2=4 

MEDIUM
IMPORTANT

The equation of normal which is at a maximum distance from-1, -1 and drawn to the circle x-12+y-22=4 is

EASY
IMPORTANT

Two tangents to the circle x2+y2=4 at the points A and B meet at P-4,0. Then the area of the quadrilateral PAOB is _____(where O is the origin)

HARD
IMPORTANT

The circle ω1 touches the circle ω:x2+y2-4x+4y+7=0 externally and has lines 2x2-xy-4x+2y=0 as normals. Find the length of the x -intercept that circle ω1 makes.

HARD
IMPORTANT

Find the slope of the focal chords of the parabola y2=32x, which are tangents to the circle x2+y2=4 

EASY
IMPORTANT

Which of the following is compound?

EASY
IMPORTANT

Cotyledons are also called-

EASY
IMPORTANT

The normal to the circle given by x2+y2-6x+8y-144=0 at (8,8) meets the circle again at the point

EASY
IMPORTANT

The normal drawn at P-1, 2 on the circle x2+y2-2x-2y-3=0 meets the circle at another point Q . Then the coordinates of Q are

HARD
IMPORTANT

The area (in square units) of the triangle formed by the tangent, normal at 1, 3 to the circle x2+y2=4 and the X - axis is

EASY
IMPORTANT

Number of normal that can be drawn from point of intersection of x-axis & line 2007x+2008y- 2009=0 to circle x2+y2=2009

MEDIUM
IMPORTANT

The radius of the circle passing through point 6, 2 and having x+y=6 as its normal and x+2y=4 as its diameter is

MEDIUM
IMPORTANT

The equation of the normal to the circle x2+y2=9 at the point 12,12 is

EASY
IMPORTANT

The line y=mx+c will be a normal to the circle with radius r and centre at a, b , if -

MEDIUM
IMPORTANT

Centre of circle whose normals are x2-2xy-3x+6y=0, is:

HARD
IMPORTANT

The equation of normal to the circle 2x2+2y2-2x-5y+3=0 at 1, 1 is

MEDIUM
IMPORTANT

The equation of normal of x2+y2-2x+4y-5=0 at (2, 1) is

EASY
IMPORTANT

The coordinates of the centre of the smallest circle passing through the origin and having y=x+1 as a diameter are

MEDIUM
IMPORTANT

The line ax+by+c=0 is normal to the circle x2+y2+2gx+2fy+d=0, if