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.