If (−4, 11) and (−6, 5) are the endpoints of a diameter of a circle, what is the equation of the circle?

The equation of the circle is given as:

Solution:

Given that,

(−4, 11) and (−6, 5) are the endpoints of a diameter of a circle

The standard form of the equation of a circle is:

Where,

(a, b) are the co-ordinates of the centre and r is the radius

To find the centre:

Find the midpoint of two given points

calculate the radius using the  distance formula

Distance between center and one end point = radius

(-5, 8) and (-4, 11)

The equation of the circle is given as:

Thus the equation of circle is found

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°