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2 years ago

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Write the equation of a circle with center (6,4) that passes through the coordinate (2,1). In your final answer, include all of

your calculations.

2 answers:

kari74 [83]2 years ago

8 0

R^2=(x-6)^2+(y-4)^2

r^2=(6-2)^2+(4-1)^2, r^2=16+9=25

(x-6)^2+(y-4)^2=25

Phantasy [73]2 years ago

6 0

Answer:

$(x-6)^2+(y-4)^2=25$

Step-by-step explanation:

It is given that,

Center of the circle = (6,4)

Circle passes through the point = (2,1)

Radius of the circle is distance between center (6,4) and point on he circle (2,1).

$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$r=\sqrt{(2-6)^2+(1-4)^2}$

$r=\sqrt{(-4)^2+(-3)^2}$

$r=\sqrt{16+9}$

$r=\sqrt{25}$

$r=5$

Standard form of a circle is

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

where, r is radius and (h,k) is center.

Substitute h=6, k=4 and r=5 in the above equation.

$(x-6)^2+(y-4)^2=5^2$

$(x-6)^2+(y-4)^2=25$

Therefore, the equation of circle is $(x-6)^2+(y-4)^2=25$ .

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Expand the polynomial and simplify: (4xy− 1 8 y^2)^2

Vinvika [58]

Answer: $4y^{2}(2x-9y)^{2}$

Step-by-step explanation:

We have the following polynomial:

$(4xy-18y^{2})^{2}$

This is a polynomial of the form $(a-b)^{2}=a^{2}-2ab+b^{2}$ . Following this rule to expand it, we have:

$(4xy)^{2}-2(4xy)(18y^{2})+(18y^{2})^{2}$

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Applying common factor $4y^{2}$ :

$4y^{2}(4x^{2}-36xy+81y^{2})$

Note the polynomial inside the parenthesis is a perfect square trinomial, which can be factored to $(2x-9y)^{2}$ . Hence, the final simplification is:

$4y^{2}(2x-9y)^{2}$

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2 years ago

How do u factor this

PilotLPTM [1.2K]

You can factor a parabola by finding its roots: if

$p(x)=x^2+bx+c$

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In order to find the roots, you can use the usual formula

$x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

In the first example, this formula leads to

$x_{1,2} = \dfrac{-2\pm\sqrt{4+4}}{2} = \dfrac{-2\pm\sqrt{8}}{2} = \dfrac{-2\pm2\sqrt{2}}{2} = 1 \pm \sqrt{2}$

So, you can factor

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

The same goes for the second parabola.

As for the third exercise, simply plug the values asking

$f(1.5)=-5.25$

you get

$f(-1.5) = 1.5c-3 = -5.25$

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3 years ago

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Gala2k [10]

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2 years ago

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defon

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2 years ago

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2 years ago