Coordinate Geometry(Senior Class Maths Study by Topics Test) : GATE Academy

Welcome to your Coordinate Geometry(Senior Class Maths Study by Topics)

NAME

PHONE NUMBER

1. Find the equation of the line passing through (2, -1) and parallel to the line 2x – y = 4.

y = x+1

y = 2x-5

y = 5x-2

y = 2/ 5x-1

2. Which of the following lines is not parallel to the line x - 2y = 5 ?

16x - 32y + 9 = 0

x - 2y + 7 = 0

x + 2y - 3 = 0

2x - 4y - 1 = 0

3. Find the equations of the straight lines joining (0, 3), (2, 0)

3x+2y-6 = 0

y-4+2

2x+6=0

x-y+6=0

4. The points of intersection between a straight line and the curve y = -x² + x + 2
give the roots of the equation x² - 2x - 1 = 0.
The equation of the line is

y = 1 + x

y = x + 3

y = x -1

y = 1 - x

5. Which of the following lines is perpendicular to the line 5x + 2y = 6?

5y -2x = 6

5x - 2y = 6

5y + 2x = -6

2y - 5x = 6

6. The equation of the line is

y = 1/2x -2

y = -2/3x + 2

y = x+2

-y = x+2

7. Your new question!

8. The line y =3x + 1 intersects the
curve y = x² -2x + 7 at the points

(-1, -2) and (3, 10)

(2, 7) and (3, 10)

(1, 4) and (2, 7)

(-2, -5) and (1, 4)

9. Find the slope from the points

-3

-2/3

10. The intercept of the line y = 3x on the x-axis is

1/3

11.

Which point is the reflection of the point (–7, 5) over the line y = –x?

(7, 5)

(5, -7)

(-5, 7)

(7, -5)

12. Find the area of the triangle formed by the vertices (4, 5), (10, 12) and (-3, 2)

3.5

4.5

13.

Line M has a y-intercept of –4, and its slope must be an integer-multiple of 1/7.

Given that Line M passes below (4, –1) and above (5, –6), how many possible slopes could Line M have?

14. Find the equations of the straight lines joining (m, 2n) and (3m, n)

3nx +my - 8mn = 0

x+2ny -7mn = n

nx + 2my -5mn = 0

nx - 3my - 10mn = 0

15. The point (1, -2)is located on the graph of a linear function.
If y increases by 3 units for each unit increase in x,
the equation of the function is

3y - x = 5

y - 3x = -5

x -3y = 5

y - 3x = 5

16. Determine the equation of a line that cuts the y-axis at -3 that is parallel to the line with equation 3x - 2y = -5

x - 3y = -9

2y + 3x = -6

2y - 3x = 6

3x - 2y = 6

17. The maximum value of y in the equation y = 1 + x - 4x² is

17/16

17/8

18. The graphs of the functions y = x³ - 9x and y = 18 - 2x² intersect at the points which the x-coordinates

-1, 0 and 3

-3, 2 and 3

0, 2 and 3

-3, 1 and 3

19. The quadrants where abcissa and ordinate have different signs are?

1st & 2nd quadrant

2nd & 4th quadrant

1st & 3rd quadrant

2nd & 3rd quadrant

20. Find the equations of the straight lines passing through the point (2, -1) and the gradient 2

y = x +1

y = x + 7

y = 4x + 9

y = 2x - 5

21.

In a coordinate system, P = (2, 7) and Q = (2, –3). Which could be the coordinates of R if PQR is an isosceles triangle?

I. (12, –3)

II. (–6, –9)

III. (–117, 2)

I, II and III

II only

II and III only

I and III only

22. A straight line y = ax intersects the parabola y = x² -5x + 6 at points P(1,2) and Q(m,n).
The values of m and n are

(-1, -2)

(-2, -4)

(6, 12)

(3, 6)

23.

In the figure, the point on segment JK that is four times as far from K as it is from J is:

(-1, 3)

(0, 2)

(2,0)

(-1/3, 7/3)

24. Which of the following points is located on the curve
y =2x² - 3x - 5 ?

(0, 5)

(1, 3)

(2, -1)

(3,4)

25.

Line Q has the equation 5y – 3x = 45. If Line S is perpendicular to Q, has an integer for its y-intercept, and intersects Q in the second quadrant, then how many possible Line S’s exist? (Note: Intersections on one of the axes do not count.)

26 out of 25