Quantitative Aptitude
MENSURATION MCQs
Regular Polygons, Triangles, Circles
Total Questions : 254
| Page 5 of 26 pages
:
Circle and line can interact in maximum three ways:
- When a line is neither touching or cutting a circle.
- When a line is touching a circle.
- When a line is cutting a circle.
Answer: Option D. -> k≥12
:
D
Since, circles are passing through the point (–1, 1) and touching X-axis, the equationof circles can be written as -
(h+1)2+(K–1)2=K2
h2+2h+2–2K=0
If h is real the Δ≥0
4- 4.1. (2 – 2K) ≥0
= 4 - 8 + 8k≥0
=8k≥4
=k≥12
:
D
Since, circles are passing through the point (–1, 1) and touching X-axis, the equationof circles can be written as -
(h+1)2+(K–1)2=K2
h2+2h+2–2K=0
If h is real the Δ≥0
4- 4.1. (2 – 2K) ≥0
= 4 - 8 + 8k≥0
=8k≥4
=k≥12
Answer: Option D. -> 5
:
D
Here the centre of circle (3, -1) must lie on the line x + 2by + 7 = 0
Therefore, 3 - 2b + 7 = 0 ⇒ b = 5
:
D
Here the centre of circle (3, -1) must lie on the line x + 2by + 7 = 0
Therefore, 3 - 2b + 7 = 0 ⇒ b = 5
Answer: Option D. -> y2−10x−6y+14=0
:
D
Let (x, y) be centre ofcircle which touch y - axis and given circle.
At any point, the radius of this circle will be equal to 'x' units. Since this circle is touching the given circle which has a radius of two units,
∴ Distance between centres of the two circles= 2 + x
⇒√(x−3)2+(y−3)2=2+x
y2−10x−6y+14=0
:
D
Let (x, y) be centre ofcircle which touch y - axis and given circle.
At any point, the radius of this circle will be equal to 'x' units. Since this circle is touching the given circle which has a radius of two units,
∴ Distance between centres of the two circles= 2 + x
⇒√(x−3)2+(y−3)2=2+x
y2−10x−6y+14=0
Answer: Option B. -> 10
:
B
Inclination of the line ←→AB is 135∘⇒Slope=tan135∘=−1
Equation of ←→AB is y−√8=−1(x+√8)⇒x+y=0
x + y = 0 passes through the centre of the circle x2+y2=25
∴ Length of the chord AB = Diameter of the circle =2×5=10
:
B
Inclination of the line ←→AB is 135∘⇒Slope=tan135∘=−1
Equation of ←→AB is y−√8=−1(x+√8)⇒x+y=0
x + y = 0 passes through the centre of the circle x2+y2=25
∴ Length of the chord AB = Diameter of the circle =2×5=10