Graph a circle with a tangent

I have to find the tangent of a circle (x-1)^2 +(y-1)^2=25 at the point (4,-3)

The solution of the tangent is 3/4x -6

But I need to graph it and it doesn't come out

[Dyuman Joshi]

This looks like a homework assignment. Show us what you have tried yet.

Answer 1

[Pratyush]

Hi Arturo,

To graph the circle ((x-1)^2 + (y-1)^2 = 25) and its tangent at the point ((4, -3)) in MATLAB, you'll first need to plot the circle and then the tangent line. The equation of the tangent line you've provided, (3/4x - 6), seems to be missing the (y) variable

The slope of the radius from the circle's center (1, 1) to the point (4, -3) is (-4/3). The slope of the tangent line, being perpendicular, is the negative reciprocal, (3/4). Using the point-slope formula, the tangent line equation is confirmed as (y = (3/4)x - 6).

MATLAB Plotting:

Circle: Use parametric equations with `cos` and `sin` for plotting, centered at (1, 1) with a radius of (sqrt{25}).

Tangent Line: Plot using the line equation y = (3/4)x - 6), across a suitable range of (x) values.

Tangency Point: Highlight the point (4, -3) on the graph.

% Circle parameters and plot
center = [1, 1]; radius = sqrt(25);
theta = linspace(0, 2*pi, 100);
x_circle = center(1) + radius * cos(theta);
y_circle = center(2) + radius * sin(theta);
plot(x_circle, y_circle, 'b-'); hold on; axis equal; grid on;

% Tangent line plot
x_tangent = linspace(-10, 10, 100);
y_tangent = (3/4) * x_tangent - 6;
plot(x_tangent, y_tangent, 'r-');

% Tangency point
plot(4, -3, 'ko');

% Labels and legend
xlabel('x'); ylabel('y');
title('Circle and its Tangent Line');
legend('Circle', 'Tangent Line', 'Tangency Point');

This script plots the circle, its tangent line at (4, -3), and marks the tangency point, visually confirming the geometric relationship.

[John D'Errico]

@Pratyush

Please don't do very obvious homework assignments for students. It does not help the student, convincing them only that they should then keep posting their homework here, with no effort made.

It does not help the teacher of that student, who now must deal with a problem that you have helped cause, because the student is now unfairly compard to other students who have actually made an effort.

It does not help this forum (and actively hurts it) because it then convinces other students to do the same.

You do everyone a disservice by doing a homework assignmet for the student.

I would note that this student has posted 4 questions. These questions are starting to show no effort at all. That means this student is no longer even bothering to try to make an effort, they are just posting a question, hoping someone will do it for them. And that means I will need to be more diligent at quickly closing future questions from this student if no effort is made.