Line tangent to a parabolaThe plane of equation x + y = 1 intersects the cone of equation z = 4 − √((x^2)+(y^2)) in a parabola. Verify that the point of coordinates (3/7, 4/7, 23/7)is on that parabola and find the equation of the line tangent to theparabola at the...
The number of common tangents to the circlex2+y2−2x−4y−4=0andx2+y2+4x+8y−5=0is ___. View Solution The product of the slopes of the common tangents of the ellipsex2+4y2=16and the parabolay2−4x−4=0is View Solution...
Step 1: Identify the parabola and the lineThe given parabola is y2=4ax and the line is x−y−a=0. Step 2: Find the points of intersectionTo find the points of intersection, we can substitute y from the line equation into the parabola equation. From the line equation, we can exp...
Solution:Wewillbeabletofindanequationofthetangentlinetassoonasweknowitsslopem.Thedifficultyisthatweknowonlyonepoint,P,ont,whereasweneedtwopointstocomputetheslope.7 Example1–Solutioncont’d ButobservethatwecancomputeanapproximationtombychoosinganearbypointQ(x,x2)ontheparabola(asinFigure2)andcomputingthe...
Find an equation in x and y for the line tangent to the parametric curve x(t) = 5e^(3t), y(t) = (t - 1)^2 at the point (x, y) = (5, 1). Find an equation in x and y for the line tangent to the parametric curve x(t) = 2e^4t...
For what values of a and b is the given line 5x + y = b tangent to the parabola y = ax^2 when x = 4? For what values of a and b is the line -4x+y=b tangent to the curve y = ax^2 when x=2? If the parabola of equation y = k - ...
Consider the parabola y=8x-x^2 .(a)Find the slope of the tangent line to the parabola at the point (1, 7).(b)Find an equation of the tangent line in part (a).y=(c)Graph the parabola and the tangent line.y2010X-20-101020一0 相关知识点: 试题来源: 解析 Giveny=8x-x^2 ...
• Now pick another point Q on the parabola and drag Q towards P to find the tangent to the curve at P. The slope of the tangent is just f (x) evaluated at x. f (x) = 2x f (2) = 4. Now, the equation of the line can be written in point-slope form like this: y ...
The slope of a parabola increases linearly with x. Slope The angle a roof surface makes with the horizontal, expressed as a ratio of the units of vertical rise to the units of horizontal length (sometimes referred to as run). The slope of an asphalt shingle roof system should be 4:12 ...
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