Solve each problem. Find the equation of the line passing through the points of intersection of the graphs of x² + y² = 20 and x² - y = 0.

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Identify the two given equations: the circle \(x^2 + y^2 = 20\) and the parabola \(x^2 - y = 0\).

Express \(y\) from the parabola equation: \(y = x^2\).

Substitute \(y = x^2\) into the circle equation to find the points of intersection: \(x^2 + (x^2)^2 = 20\), which simplifies to \(x^2 + x^4 = 20\).

Solve the resulting equation for \(x\) to find the \(x\)-coordinates of the intersection points, then use \(y = x^2\) to find the corresponding \(y\)-coordinates.

Use the two points of intersection to find the equation of the line passing through them by calculating the slope \(m = \frac{y_2 - y_1}{x_2 - x_1}\) and then using the point-slope form \(y - y_1 = m(x - x_1)\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

10m

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Finding Points of Intersection

To find where two graphs intersect, solve their equations simultaneously. This involves substituting one equation into the other or using algebraic methods to find common solutions (x, y) that satisfy both equations.

Equation of a Line Through Two Points

Once two points are known, the equation of the line passing through them can be found using the slope formula and point-slope form. The slope is the change in y over the change in x, and the line equation can be expressed in forms like y = mx + b.

Substitution Method in Systems of Equations

The substitution method involves solving one equation for one variable and substituting that expression into the other equation. This simplifies the system to a single-variable equation, making it easier to find the intersection points.

Solve each problem. Find the equation of the line passing through the points of intersection of the graphs of x2 + y2 = 20 and x2 - y = 0.