This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Right bazuunelson, let's go. 1) Find equation of circle with center (0,0) radius 5 Step 1: Recall the standard equation of a circle. The equation of a circle with center (h,k) and radius r is given by: (x-h)^2 + (y-k)^2 = r^2 Step 2: Substitute the given values. Given center (h,k) = (0,0) and radius r = 5. Substitute h=0, k=0, and r=5 into the equation: (x-0)^2 + (y-0)^2 = 5^2 Step 3: Simplify the equation. x^2 + y^2 = 25 The equation of the circle is x^2 + y^2 = 25. 2) State equation of tangent to x^2 + y^2 = 25 at (3,4) Step 1: Identify the center and radius squared of the circle. The given equation of the circle is x^2 + y^2 = 25. This is a circle centered at the origin (0,0) with r^2 = 25. Step 2: Use the formula for the tangent to a circle centered at the origin. For a circle x^2 + y^2 = r^2, the equation of the tangent at a point (x_1, y_1) on the circle is given by: x x_1 + y y_1 = r^2 Step 3: Substitute the given point and r^2 value. The point of tangency is (x_1, y_1) = (3,4) and r^2 = 25. Substitute x_1=3, y_1=4, and r^2=25 into the tangent equation: x(3) + y(4) = 25 Step 4: Simplify the equation. 3x + 4y = 25 The equation of the tangent is 3x + 4y = 25. Send me the next one 📸