10th GRADE MATH SOLUTION EXERCISE 5.5 part5

This page 10th grade math solution exercise 5.5 part5 is going to provide you solution for every problems that you find in the exercise no 5.5

10th grade math solution exercise 5.5 part5

(16) Find the coordinates of the foot of the perpendicular from the origin on the straight line 3x + 2 y = 13

Solution:


In the page10th grade math solution exercise 5.5 part5 we are going to see the solution of next problem

(17) If x + 2y = 7 and 2 x + y = 8 are the equations of the lines of two diameters of a circle,find the radius of the circle if the point (0,-2) lies on the circle.

Solution:

To find the center of the circle we need to find the point of intersection of two given lines

x + 2y = 7 ---- (1)

2 x + y = 8 ---- (2)

(1) - (2)

(1) x 2 => 2x + 4y = 14

              2x  + y = 8

               (-)  (-)  (-)

        ----------------- 

              3y = 6

               y = 2

 Substitute y = 2 in the first equation

        x + 2(2) = 7

         x + 4 = 7 

            x = 7 - 4

            x = 3

the point of intersection is (3,2)

Distance between the points (3,2) and (0,-2)

                     = √(x - x₁)²  + (y - y₁)²

                     = √(0 - 3)²  + (-2 - 2)²

                     = √(- 3)²  + (-4)²

                     = √9  + 16

                     = √25

                     = 5 units




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