Normal and Condition of Normality - Basic Quiz

Normal and Condition of Normality - Basic Quiz         

Dear Readers,

Mathematics is an important subject in SSC,DSSB & Other Exams. .

Q1. The normal to the circle x^2+y^2-3x-6y-10=0 at the point (– 3, 4), is :

•  2x+9y-30=0
•  9x-2y+35=0
•  2x-9y+30=0
•  2x-9y-30=0

Solution
2x+9y-30=0

Q2.The equation of normal to the circle 2x^2+2y^2-2x-5y+3=0 at (1, 1) is:

•  2x+y=3:
•  x-2y=3
•  x+2y=3
•  None of these

Solution
x+2y=3

Q3.  The normal at the point (3, 4) on a circle cuts the circle at the point ( –1, –2). Then the equation of the circle is :

•  x^2+y^2+2x-2y-13=0
•  x^2+y^2+14x+6y+2=0
•  x^2+y^2-2x+2y+12=0
•  x^2+y^2-2x-2y+14=0

Solution
x^2+y^2+14x+6y+2=0

Q4. The line λx+μy=1 is a normal to the circle 2x^2+2y^2-5x+6y-1=0 if

•  5λ-6μ=2
•  4+5μ=6λ
•  4+6μ=5λ
•  None of these

Solution
4+6μ=5λ

Q5.The equation of a normal to the circle x^2+y^2+6x+8y+1=0 passing through (0, 0) is

•  3x+4y=0
•  3x-4y=0
•  4x-3y=0
•  4x+3y=0

Solution
 4x-3y=0

Q6. The equation of the normal at the point (4, – 1) of the circle x^2+y^2-40x+10y=153 is

•  x+4y=0
•  x-4y=0
• 4x+y=3
•  4x-y=0

Solution
x+4y=0

Q7.The equation of the normal to the circle x^2+y^2-4x+6y=0 at (0, 0) is

•  3x-2y=0
•  2x-3y=0
•  3x+2y=0
•  2x+3y=0

Solution
3x+2y=0