Question

The ends of hypotenuse of a right angled triangle are (5)
0).(-5, 0) then the locus of third vertex is
1 2? + y = 25
2 2 + y = 5
3 x2 - y2 = 25
4 22 - y = 5​

Answer 1

Answer:

x2 - y2 = 25

Step-by-step explanation:

I hope it helps you

Answer 2

Step-by-step explanation:

• So if we plot a graph, we have the point (5,0) on the x axis and (-5,0) on the y axis. If both the points are joined to form a triangle then it will be a right angled triangle. So it can be A,B and C where BC is the base. Now coordinates of A will be (x,y), coordinates of B will be (-5,0) and coordinates of C will be (5,0).
• So we have AC^2 + AB^2 = BC^2
•     So BC = 10
• So the distance formula will be
•                       D = (x2 – x1)^2 + (y2 – y1)^2
•   Applying this formula we get
•    [(x + 5)^2 + (y – 0)^2]^2 + [(x – 5)^2 + (y – 0)^2]^2 = 10^2
• Applying (a + b)^2 and (a – b)^2
• So x^2 + 10x + 25 + y^2 + x^2 – 10x + 25 + y^2 = 100
•       So 2x^2 + 2y^2 + 50 – 100 = 0
•             2x^2 + 2y^2 - 50 = 0
•    Taking 2 common we get   2(x^2 + y^2 – 25) = 0
•            Or x^2 + y^2 – 25 = 0
• Therefore the locus of the point is x^2 + y^2 = 25

Reference link will be

https://brainly.in/question/6833300