The equation of a circle is (x - 3)2 + (y + 2)2 = 25. The point (8, -2) is on the circle.What is the equation of the line that is tangent to the circle at (8, -2)?

Answers

Answer 1

Answer:

The equation of the line that is tangent to the circle at (8, -2) is:

$x=8$

Step-by-step explanation:

We know that the line which is tangent at a point on a circle is perpendicular to the line joining the center of the circle and that point.

Here we are given the equation of a circle as:

$(x-3)^2+(y+2)^2=25$

The center of the circle is at: (3,-2)

( Since, the standard form of a circle with center at (h,k) and radius r is given by:

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

Also, the equation of a line joining (3.-2) and (8,-2) is given by:

$y-(-2)=(-2-(-2))/(8-3)* (x-3)\n\ni.e.\n\ny+2=(-2+2)/(5)* (x-3)\n\ni.e.\n\ny+2=(0)/(5)* (x-3)\n\ni.e.\ y+2=0\n\ni.e.\ y=-2$

Also, we know that the slope of this line is zero.

Also, we know that if two lines are perpendicular with slope m and m' respectively then,

$m\cdot m'=-1\n\ni.e.\n\nm'=(-1)/(m)$

Hence, we get that the slope of the tangent line is:

$(-1)/(0)$

Also, we know that:

The equation of a line with given slope m' and a passing through point (a,b) is given by:

$y-b=m'(x-a)$

Here (a,b)=(8,-2)

and $m'=(-1)/(0)$

i.e. the equation of the tangent line is:

$y-(-2)=(-1)/(0)(x-8)\n\ni.e.\n\ny+2* 0=-1(x-8)\n\ni.e.\n\n-1* (x-8)=0\n\ni.e.\n\n(x-8)=0\n\ni.e.\n\nx=8$

Answer 2

Answer: Hello,

O=(3,-2) is the center of the circle and 5 its radius.

P=(8,-2)
The line OP is parallele to ox axis so then tangent is parallele to oy axis
Its equation is x=8.

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Answers

In the given question, there are several information's of immense importance. The information's are:
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Which point lies on a circle that is centered at A(-3, 2) and passes through B(1, 3)?C(-1, -2)

D(-6, 3)

E(-3, -3)

F(-2, 6)

Answers

The equation of a circle:
$(x-h)^2+(y-k)^2=r^2$
(h,k) - the coordinates of the center
r - the radius

$\hbox{the center: } A(-3,2) \nh=-3 \n k=2 \n \n\hbox{the equation:} \n(x+3)^2+(y-2)^2=r^2 \n \n\hbox{the circle passes through B(1,3)} \nx=1 \n y=3 \n \Downarrow \n(1+3)^2+(3-2)^2=r^2 \n4^2+1^2=r^2 \n16+1=r^2 \n17=r^2 \n \n\hbox{the equation is:} \n(x+3)^2+(y-2)^2=17$

Plug the coordinates of the points into the equation and check:
$C(-1,-2) \n(-1+3)^2+(-2-2)^2=17 \n2^2+(-4)^2=17 \n4+16=17 \n20=17 \nnot \ true \n \nD(-6,3) \n(-6+3)^2+(3-2)^2=17 \n(-3)^2+1^2=17 \n9+1=17 \n10=17 \nnot \ true$

$E(-3,-3) \n(-3+3)^2+(-3-2)^2=17 \n0^2+(-5)^2=17 \n25=17 \nnot \ true \n \nF(-2,6) \n(-2+3)^2+(6-2)^2=17 \n1^2+4^2=17 \n1+16=17 \n17=17 \ntrue$

The answer is F(-2,6).

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Answers

$f(x)=x^3-2x^2+5x+1\n f'(x)=3x^2-4x+5\n3x^2-4x+5=0\n\Delta=(-4)^2-4\cdot3\cdot5=16-60=-44$
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Max travels to see his brother's family by car. He drives 216 miles in 4 hours. What is his rate in miles per hour? B) Suppose he makes two stops of 10 minutes each during his journey. Will he be able to reach the town in 4 hours if he keeps the speed the same?

Answers

Answer:

54 miles/hour

If he made two stops of 10 minutes each and maintains the same speed, it would take him more than 4 hours to reach the town as the time speed would have been extended by 20 minutes.

Step-by-step explanation:

The rate of change of distance with time is called speed and it is measured in miles per hour. Mathematically,

Speed = Distance/time

His rate in miles per hour is his speed

= 216/4

= 54 miles per hour

Answer:

Rate in miles per hour: 54 miles per hour

Step-by-step explanation:

Which is an equation of a circle with center (5, 0) that passes through the point (1, 1)? HELP ME PLEASE!! Answer Choices:

A.) (x - 1)2 + (y - 1)2 = 17
B.) (x + 5)2 + y2 = 17
C.) (x + 5)2 + y2 = 24
D.) (x - 5)2 + y2 = 17

Answers

a) first we will calculate the distance between center and given point because this is the radius of circle:

$d=√((1-5)^2+(1-0)^2)\n \n d=√((-4)^2+1)=√(17)$

b) Now we will write the equation of the circle:

$\boxed{\boxed{(x-5)^2+y^2=17}}$

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