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3 years ago

Helppppppp meeeeeee I don’t understanddddd

Mathematics

1 answer:

scoundrel [369]3 years ago

5 0

Answer:

DF = 9.5

Step-by-step explanation:

Given 2 secants from an external point to the circle, then

The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is

DE × DF = DC × DB

5(5 + x) = 5(5 + 4.5) ← divide both sides by 5

5 + x = 5 + 4.5

5 + x = 9.5 ( subtract 5 from both sides )

x = 4.5

Then

DF = DE + EF = 5 + 4.5 = 9.5

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2 years ago

Find the equation of the circle with a diameter whose end points are (-1,-2) and (-3,2)

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Answer:

The equation of the circle with a diameter whose end points are (-1,-2) and (-3,2) is

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Step-by-step explanation:

Explanation:-

Step 1:-

The equation of the circle having center and radius is

$(x-h)^2+(y-k)^2=r^2$

here center is (h,k) and radius is r

Given diameter whose end points are (-1,-2) and (-3,2)

The diameter of the circle is passing through the center of the circle

so center of the circle = midpoint of two end points

$(\frac{-1 +(-3) }{2} ,\frac{-2+2 }{2} )$

$(-2,0)$

therefore center (h,k) = (-2,0)

Step 2:-

we have to find the radius of the circle

the radius of the circle = the distance from center to the one end point

i.e., C P = r

Given one end point is P(-3,2) and center C(-2,0)

The distance formula of two points are

$\sqrt{(x_{2}-x_{1} ) ^{2}+ (y_{2}-y_{1} ) ^{2}}$

$r=\sqrt{{(-3)-(-1) ) ^{2}+ (2-(-2)) ^{2}}$

$r=\sqrt{5}$

Step 3:-

center (h,k) = (-2,0) and

radius $r=\sqrt{5}$

The standard form of circle equation

$(x-h)^2+(y-k)^2=r^2$

$(x-(-2))^2+(y-0)^2=\sqrt{5} ^2$

on simplification is

$x^{2} +y^{2}+4 x-1=0$

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2 years ago