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A tangent line is drawn to the circle with equation x^2 + y^2 = a^2 at a point (x0, y0), in the first quadrant. The line segment of the tangent line, in the first quadrant, forms a right triangle with the coordinate axes; The following figure illustrates the situation under consideration: a) Find the equation of the line tangent to the graph of x^2 + y^2 = a^2 at the point (x0, y0), located in the first quadrant. b) Write the formula for the area of the right triangle, formed by the tangent line segment and the coordinate axes, as a function of a single variable. c) Find the coordinates of the point (x0, y0), for which the area of the right triangle is maximum.

A tangent line is drawn to the circle with equation x^2 + y^2 = a^2 at a point (x0, y0), in the first quadrant. The line segment of the tangent line, in the first quadrant, forms a right triangle with the coordinate axes; The following figure illustrates the situation under consideration: a) Find the equation of the line tangent to the graph of x^2 + y^2 = a^2 at the point (x0, y0), located in the first quadrant. b) Write the formula for the area of the right triangle, formed by the tangent line segment and the coordinate axes, as a function of a single variable. c) Find the coordinates of the point (x0, y0), for which the area of the right triangle is maximum.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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A tangent line is drawn to the circle with equation x^2 + y^2 = a^2 at a point (x0, y0), in the first quadrant. The line segment of the tangent line, in the first quadrant, forms a right triangle with the coordinate axes; The following figure illustrates the situation under consideration:

a) Find the equation of the line tangent to the graph of x^2 + y^2 = a^2 at the point (x0, y0), located in the first quadrant.

b) Write the formula for the area of the right triangle, formed by the tangent line segment and the coordinate axes, as a function of a single variable.

c) Find the coordinates of the point (x0, y0), for which the area of the right triangle is maximum.

Problem 3 A tangent line is drawn to the circle with equation 22 +y² = a² at a point (*0, Y0), in the first quadrant. The line segment of the tangent line, in the first quadrant, forms a right triangle with the coordinate axes; The following figure illustrates the situation under consideration: Porción recta tangente. a Cuarto de circunferencia a a) Find the equation of the line tangent to the graph of a2+y² = a² at the point (o, Y0), located in the first quadrant. b) Write the formula for the area of the right triangle, formed by the tangent line segment and the coordinate axes, as a function of a single variable. c) Find the coordinates of the point (x0, Y0), for which the area of the right triangle is maximum.
Transcribed Image Text:Problem 3 A tangent line is drawn to the circle with equation 22 +y² = a² at a point (*0, Y0), in the first quadrant. The line segment of the tangent line, in the first quadrant, forms a right triangle with the coordinate axes; The following figure illustrates the situation under consideration: Porción recta tangente. a Cuarto de circunferencia a a) Find the equation of the line tangent to the graph of a2+y² = a² at the point (o, Y0), located in the first quadrant. b) Write the formula for the area of the right triangle, formed by the tangent line segment and the coordinate axes, as a function of a single variable. c) Find the coordinates of the point (x0, Y0), for which the area of the right triangle is maximum.
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