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Your answer is INCORRECT:Which of the following equations belongs to circle satisfying the given conditions:The circle is tangent to the x-axis and to the y-axis: I...

Question

Your answer is INCORRECT:Which of the following equations belongs to circle satisfying the given conditions:The circle is tangent to the x-axis and to the y-axis: Its center is in the 3rd quadrant: Its diameter is 0 units ongy _ 10x - 10y +25 = 0Cr_ +y+l0x+ 10y+25 = 0+ 10x + I0y - 100 = 0+y+l0x+ l0y_ 25 = 0Y + 20x+ 20y+25 = 0None of these

Your answer is INCORRECT: Which of the following equations belongs to circle satisfying the given conditions: The circle is tangent to the x-axis and to the y-axis: Its center is in the 3rd quadrant: Its diameter is 0 units ong y _ 10x - 10y +25 = 0 Cr_ +y+l0x+ 10y+25 = 0 + 10x + I0y - 100 = 0 +y+l0x+ l0y_ 25 = 0 Y + 20x+ 20y+25 = 0 None of these



Answers

Write an equation of a circle with the given center and radius. Check your answers.
$$
(0,0), 10
$$

Problem. We're given the line three x plus four y equals 10 and we're told that a circle centered at +00 is tension to the line. Three expose for y equals 10 and we're trying to find the radius of the circle. So let's draw this scenario out really quickly to the best of our ability. So we know that this is our coordinate plane and let's draw our three X plus four y equals 10 3 experts for I equals 10 is gonna look something like, um, something like this. A student at MC. Why? Cause I'm exposed reform for us. So we know how autograph it So three x was for y equals 10 is gonna be for why my equals minus three X plus 10. And so if you divide out by four on both sides, you're gonna get your image MX plus B form. Let's just get rid of this Ford. So we have 10 10 coming for around here or something. This is just a general sketch. So why it goes negative. Three extras for was 10 over for something like this, and we're trying to find this circle at which is tangent to at a single point. So this is with the one point of intersection. So basically what we're doing this problem is we try to find the distance between the 1.0.0 comma zero and the line three X plus four equals tech will. Generally, if you have a line a X, please be why this is important for me to remember. Plus C equals zero and is trying to find the distance from X zero comma y zero. To that line, the distance is gonna be equivalent to the absolute value. Or like the distance of a equal a egg zero plus B y zero plus c all over square root a squared plus B squared. Now, if we take a look at this for right here, let's try to put in the extra b y plus C equals zero for So in order to do that, you just tracked out the 10 and you get three actually swore Y minus 10 is equal to zero our age. Three B's for sees negative 10 and RX zero is zero R Y 00 So this basically simplifies to, uh, absolute value of 10 negative 10 over Square root three squared plus four squared. And if you send a file is the distance that you get is you get a distance of two. So the, um, circle is, ah, circle of radius to that means it's equation is gonna be X squared plus y squared plus two squared, which is four. And the answer choice that corresponds to this is answer choice B M Pretty on his answer Choice B s so answer Choice B is the correct answer.

We need to find the center and the radius of the given circle. So we're going to first have to complete the square. So we have x squared minus 10. X. Leave some space plus y squared plus two. Y leave some space. Move the 25 over. So we take the middle term which is negative 10 divided by two square it. So that's plus 25. So we have to add 25 to the other side And we have to take two divided by two square it That's one. So we add one to both sides. So this simplifies to be X -5 squared plus. Why? Plus one Squared is equal to one. Sorry, equation of our circle is x minus H squared plus y minus k squared is equal to r squared. So our center comes from hk so h corresponds with five. The second parenthesis was why minus a negative one before it was fixed. Okay is negative one. So our center is at five negative one or radius comes from r squared. So we have R squared is equal to one. We take the positive square root and we get that the radius is equal to one.

We need to find the equation off the circle whose radius is given to be five. And it is also given that the circle eyes in the First Quadrant and the 10 Gent two on the circle has tangent, towboat, X axis and the Y exists. Since the circle has tangent to pour tax sexes and Y axes so and its radius is equal to five. So the circle touches the 50.5 and the circle patches the 0.50 So it's center. Realize at point. If I fight now, we have the standard equation of the circle scare off X minus H plus scare off by minus K is equal to be ask it were at Kerry presented the coordinate of the center of the circle, and our represent the radius of the circle, never putting the value of the coordinator of the center of circle and radius. It will reduces to X minus five scare plus y minus five. Scare is equal to be 25 so this is the required equation off the circle

We need to find the center and the radius of the given circles. We're going to need to complete the square. So we have X squared plus three X. Leave some space plus y squared minus five wide. Leave some space equals move the 25 4th over. So that's minus 25/4. We're gonna take the middle term three divided by two and square it so it becomes 94 So we're gonna add that to both sides. I think you're gonna take the middle term of the wise, Divide by two and Square it. So that becomes plus 25/4. So we have that to both sides. So this simplifies to be X plus three halves squared plus why? Minus five halves squared is equal to 9/4. Sorry, equation of our circle is x minus h squared plus y minus k squared is equal to r squared. Our center comes from hk So this used to be X -A -3 has before it was fixed. So age corresponds to -3. House. Okay, is positive 5/2. R radius comes from r squared, so we have R squared is equal to 9/4. We take the positive square root of both sides, and we get our is equal to 3/2.


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