Question

a circle has equation x2 + y2 = 25 the circle passes through the points a b c and d comeete the coordinates for each

Answer 1

SOLUTION

COMPLETE QUESTION

A circle has equation x² + y² = 25

The circle passes through the points A, B, C and D.

Complete the coordinates for A, B, C and D.

A. (5,_)

B.(_,-5)

C. (_,0)

D. (0,_)

EVALUATION

Here the given equation of the circle is

$\sf {x}^{2} + {y}^{2} = 25 \: \: - - - (1)$

For the point A(5,_)

We have x = 5

From Equation 1 we get

$\sf {5}^{2} + {y}^{2} = 25$

$\displaystyle \sf{ \implies 25 + {y}^{2} = 25}$

$\displaystyle \sf{ \implies {y}^{2} =0 }$

$\displaystyle \sf{ \implies y = 0}$

So we have A(5,0)

For the point B(_, - 5)

We have y = - 5

From Equation 1 we get

$\displaystyle \sf{ {x}^{2} + {( - 5)}^{2} = 25}$

$\displaystyle \sf{ \implies {x}^{2} + 25 = 25}$

$\displaystyle \sf{ \implies {x}^{2} = 0}$

$\displaystyle \sf{ \implies x = 0}$

So we have B(0, - 5)

For the point C(_, 0)

We have y = 0

From Equation 1 we get

$\sf {x}^{2} + {0}^{2} = 25$

$\displaystyle \sf{ \implies {x}^{2} + 0 = 25}$

$\displaystyle \sf{ \implies x = \pm 5}$

Either C(5,0) or C( - 5,0)

Since A is (5,0)

So we have C( - 5,0)

For the point D(0,_)

We have x = 0

From Equation 1 we get

$\displaystyle \sf{ \implies {0}^{2} + {y}^{2} = 25}$

$\displaystyle \sf{ \implies 0 + {y}^{2} = 25}$

$\displaystyle \sf{ \implies {y}^{2} = 25}$

$\displaystyle \sf{ \implies y = \pm \: 5}$

Either D(0,5) or D(0, - 5)

Since B is (0, - 5)

So we have D(0,5)

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ Leon created a scale drawing of the school library in his art class. In the scale drawing, the length of the library is ...

https://brainly.in/question/36658582

2. The scale on a map is 2cm = 1km if the distance show on the map is 14 cm, what is the actual distance

https://brainly.in/question/36868303

Answer 2

Given :  A circle has equation x² + y² = 25

The circle passes through the points A, B, C and D.

Complete Question is :

To Find : Complete the coordinates for A, B, C and D.

A. (5,_)

B.(_,-5).

C. (_,0)

D(0,_)

Solution:

Every point on the circle satisfy the equation of the circle.

x² + y² = 25

A. (5,_)

=> x= 5  y = ?

=> 5² + y² = 25

=> 25 + y² = 25

=> y² = 0

=> y = 0

Hence A  is ( 5 , 0)

B.(_,-5)

=> x= ?  y = -5

=> x² +(-5)² = 25

=>  x² + 25   = 25

=>  x² = 0

=> x = 0

Hence B  is ( 0 , -5)

C. (_,0)

=> x= ?  y = 5

=> x² +0² = 25

=>  x² + 0   = 25

=>  x² = 25

=> x = ±5

Hence C can  be (5 , 0) or ( - 5 , 0)

But A is (5 , 0)

Hence C  is ( -5 , 0)

D(0,_)

=> x= 0  y = ?

=> 0² + y² = 25

=> 0 + y² = 25

=> y² =25

=> y = ±5

Hence D can  be (0 , 5) or ( 0, - 5)

But B is (0 ,-5)

Hence D  is ( 0 , 5)

A  is ( 5 , 0)  , B  is ( 0 , -5) ,  C  is ( -5 , 0) and D   is ( 0 ,5)

Learn More:

Equation of the circle which is such that the lengths of the tangents ...

brainly.in/question/13068835

find the equation of circle which passed through origin and cuts off ...

brainly.in/question/2075668