MCQ: Coordinate Geometry - 2 - SSC CGL MCQ

Since the two points A and B are on circle O, the distance between OA and OB will be equal.
Therefore, using the distance formula we get

Squaring both sides,
(x−2)² + 4 = 4 therefore x = 2
Hence, x = 2 is the correct answer.

¹³​​​​​
= x² + 25 = 169
= x² = 169 - 25 = 144
∴ x = ±12

• The given line is:
• 3x + 4y + 7 = 0
• Step 1: Find the slope of the given line:
• Rewrite as y = mx + c: y = -3/4 * x - 7/4
• So, the slope (m) is: -3/4.
• Step 2: Use the point-slope form for the new line passing through (1, 2):
• y - 2 = -3/4 (x - 1)
• Step 3: Simplify the equation:
• y - 2 = -3/4 * x + 3/4 y = -3/4 * x + 3/4 + 2 y = -3/4 * x + 11/4
• Step 4: Convert to general form:
• Multiply by 4: 4y = -3x + 11 Rearrange: 3x + 4y = 11

According to the question, we are given a region bounded by the curves y = x² and y = 2x² − 1. The region is partitioned by drawing two distinct lines such that they divide the regions into two parts at least. The total number of regions, n, generated by these lines is unknown. To find the value of n we need to analyse the region.
Now, we draw the lines, as follows,

The two curves will meet when both the function have same value for any given x.

So, the equation will be x² = 2x² − 1.
On solving this equation we get
2x² − x² = 1x² = 1x = ±1
So, from the above simplification, we got the points x = 1 and x = −1. 
So, there is only one region bounded by the given curves, and if we partition this region using two lines we can have 4 or 5 regions based on how the lines are drawn.
Therefore, the value of 'n' can be 5 but not 6.

Given equation, ax − 4y = −6
Slope of the equation 

a = -6

Using Distance formula

Given points: (– 5, 7) and (– 1, 3)
Distance between the points will be (x₁, y₁) and (x₂, y₂).
We know that,

Hence, the correct answer is 4√2.

x + y + 1 = 0 and 2x – y + 5 = 0
then x+y = -1, 2x-y=-5
by verification method, option :b (-2,1)
-2+1 = -1, -4-1 = -5

• As we know pair of alternate angles are equal 
• Hence,
• ∠FGC = ∠CHI = 80 degrees 

We assume that,

x₁ = 2, y₁ = 5, x₂ = 5 & y₂ = 2 Point C: (x,y)
Line divides the line segment in the ratio m₁ : m₂  
This is known as internal division.

Point C satisfies the equation of line.

The vertices of a triangle ABC be
(4, 4), (3, 5) and (−1,−1)
Distance between two points 

Distance between

Distance between

Distance between 

AC² = 50
AB² + AC² = 2 + 50 = 52
⇒ AB² + AC² = BC²
It follows Pythagoras theorem so, triangle is a right angle triangle.

When two or more lines cross each other in a plane, they are called intersecting lines. The intersecting lines share a common point, which exists on all the intersecting lines, and is called the point of intersection.
Hence, the correct answer is O.

From the given figure, we know that the sum of all the angles of a linear pair is always 180°. Here,  form a linear pair.

Hence, option B is the correct answer.

Given that,
∠BOA = 45°
∠AOD = a°
∠DOB = b°

Now, k || m || l
a°+b°=45° (given in question) as they form interior alternate angles with the transversal.
Hence, value of a°+b° is 45°.

equation  9x − 12y = 108
Intersection of y−axis (by putting x = 0)
−12y = 108
y = −9
intersection of x − axis(by putting y = 0)
9x = 108
x = 12

Using pythagoras theorm,
The length of the intercept is