Worksheet on Locus of a Moving Point

To practice the questions given in the worksheet on locus of a moving point we need to follow the method of obtaining the equation of the locus to solve these questions.


1. A point moves in such a manner that three times of its abscissa is greater by 5 than two times of its ordinate; find the equation of its locus.

2. If twice the abscissa of a point moving in the xy-plane always exceeds three times its ordinate by 1, show that the locus of the point is a straight line.

3. A point moves in the xy-plane in such a way that its distance from the x-axis and the point (1, -2) are always equal. Find the equation of its locus.

4. A point moves in the xy-plane in such a way that its distance from the point (4, 0) is always equal to its distance from the y-axis. Find the equation to the locus of the moving point.

5. A point moves such that its distance from the y –axis is equal to its distance from the point (2, 0). Find its locus and identify the nature of the conic.

6. A point P (x, y) moves in the xy-plane in such a way that its distance from the point (0, 4) is equal to 2/3 rds of its distance from the x-axis ; find the equation to the locus of P.

7. Find the equation to the locus of a moving point which is equidistant from the points (2,3) and (4,-1).

8. Find the locus of a point which moves so that the sum of the squares of its distance from the points (3, 0) and (-3, 0) is always equal to 50.

9. A point moves in a plane such that its distance from the point (2, 3) exceeds its distance from the y-axis by 2. Find the equation to the locus of the point.

10. A point so moves that the sum of squares of its distance from (a, 0) and (-a, 0) is 2b2. Find the equation to the locus of the moving point. If a = b then what will be locus of the moving point?

11. The ratio of the distance of a moving point from the points (3, 4) and (1, -2) is 2 : 3; find the locus of the moving point.

12. A (1, 2) and B (5, -2) are two given points on the ey-planes, on which C is a moving point, such that the numerical value of the area of ΔCAB is 12 square units. Find the equation to the locus of C.


Answers for the worksheet on locus of a moving point are given below to check the exact answers of the above questions on locus.


Answers:

1. 3x – 2y = 5.

3. x2 – 2x + 4y + 5 = 0.

4. y2 = 8 (x – 2).

5. y2 = 4(x – 1), parabola.

6. 9x2 + 5y2 – 72y + 144 = 0.

7. x – 2y = 1.

8. x2 + y2 = 16.

9. (y – 3)2 = 8x.

10. x2 + y2 = b2 – a2; x2 + y2 = 0 i.e., the moving point represent the origin.

11. 5x2 + 5y2 – 46x – 88y + 205 = 0.

12. x + y = 9 or, x + y + 3 = 0.

 Locus




11 and 12 Grade Math

From Worksheet on Locus of a Moving Point to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Worksheet on Word Problems on Fractions | Fraction Word Problems | Ans

    Jul 16, 24 02:20 AM

    In worksheet on word problems on fractions we will solve different types of word problems on multiplication of fractions, word problems on division of fractions etc... 1. How many one-fifths

    Read More

  2. Word Problems on Fraction | Math Fraction Word Problems |Fraction Math

    Jul 16, 24 01:36 AM

    In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

    Read More

  3. Worksheet on Add and Subtract Fractions | Word Problems | Fractions

    Jul 16, 24 12:17 AM

    Worksheet on Add and Subtract Fractions
    Recall the topic carefully and practice the questions given in the math worksheet on add and subtract fractions. The question mainly covers addition with the help of a fraction number line, subtractio…

    Read More

  4. Comparison of Like Fractions | Comparing Fractions | Like Fractions

    Jul 15, 24 03:22 PM

    Comparison of Like Fractions
    Any two like fractions can be compared by comparing their numerators. The fraction with larger numerator is greater than the fraction with smaller numerator, for example \(\frac{7}{13}\) > \(\frac{2…

    Read More

  5. Worksheet on Reducing Fraction | Simplifying Fractions | Lowest Form

    Jul 15, 24 03:17 PM

    Worksheet on Reducing Fraction
    Practice the questions given in the math worksheet on reducing fraction to the lowest terms by using division. Fractional numbers are given in the questions to reduce to its lowest term.

    Read More