The angle between the rectangular hyperbolas x y=6 and x^2-y^2=5 at (3,2) is (a) 0^∘ (b) 90^∘ (c

step 1 So we have to find the angle between these two hyperbolas, these two rectangular hyperbolas at t

The angle between the rectangular hyperbolas x y=6 and...

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Key Concepts

Implicit Differentiation

Implicit differentiation is a technique used to find the derivative of a function when it is presented in an implicit form, i.e., with x and y intermixed rather than having y isolated on one side. This method is essential for finding the slopes of tangent lines to curves that are defined by such equations.

Tangent Lines to Curves

The concept of tangent lines involves determining the line that just touches a curve at a single point without crossing it immediately. The slope of the tangent line, calculated via differentiation, provides crucial information about the behavior of the curve at that point and is key to analyzing the angle at which two curves intersect.

Angle Between Two Lines

The angle between two curves at an intersection point is defined as the angle between their respective tangent lines. This angle can be determined using the formula for the angle between two lines: tan(?) = |(m1 - m2) / (1 + m1 * m2)|, where m1 and m2 are the slopes of the tangent lines. This method is widely applicable in differential calculus and analytical geometry.

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