Suppose the Line $x - 7 y + 55 = 0$

question 11

Multiple Choice

Suppose the line $x - 7 y + 55 = 0$ intersects the circle $x ^ { 2 } - 10 x + y ^ { 2 } - 10 y = - 25$ at points $P$ and $e$ . Find the length of the chord $\overline { P Q }$ .

• A) \(\sqrt { 5 }\)
• B) \(5 \sqrt { 2 }\)
• C) \(2 \sqrt { 5 }\)
• D) \(36 \sqrt { 2 }\)
• E) \(6 \sqrt { 2 }\)

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Definitions:

Calcium Carbonate

A chemical compound with the formula CaCO3, found in rocks such as limestone, chalk, and marble, and is the main component of shells of marine organisms.

Chalk Formation

A type of limestone characterized by its fine, white, porous structure, formed from the accumulation of microorganisms' calcite shells.

Microscopic Organisms

Tiny life forms, not visible to the naked eye, including bacteria, protozoa, and certain types of fungi and algae.

Calcium Carbonate

A chemical compound with the formula CaCO3, found in rocks such as limestone, chalk, and marble, and is a major component of shells of marine organisms, snails, and eggs.