Answer:
<h2>QT = 21</h2><h2>SV = 41</h2>
Step-by-step explanation:
From the diagram, it can be seen that TR is parallel to RV. This means that TR = RV. Given TR = 17 and RV = 3x+2
3x+2 = 17
3x = 17-2
3x = 15
x = 5
RV = 3(5)+2 = 17
QV = 4x+1 = 4(5)+1
QV = 21
Using Pythagoras theorem on ΔQRV to get RQ
QV² = QR²+RV²
21² = QR²+17²
QR² = 21²-17²
QR = 12.33
Using Pythagoras theorem on ΔQRT to get QT
From ΔQRT,
QT² = QR²+TR²
QT² = 12.33²+17²
QR² = 152.0289+289
QT² = 441.0289
QT =21
Since TS = 9(5)-4 = 41
Using Pythagoras theorem on ΔTRS
From ΔTRS,
TS² = RS²+TR²
41² = RS²+17²
RS² = 41²-17²
RS² = 1392
RS = 37.31
Similarly Using Pythagoras theorem on ΔRSV
From ΔRSV,
SV² = RV²+RS²
SV² = 17²+37.31²
SV² = 1681.0361
SV = 41
$2.25x+$3.50=$35
so, $35-$3.50=$31.50
Then you divide $31.50 by $2.25
That equals 14
So, x=14
In the general case in Cartesian coordinates, you would use the definition of a parabola as the locus of points equidistant from the focus and directrix. The equation would equate the square of the distance from a general point (x, y) to the focus with the square of the distance from that point to the directrix line.
Suppose the focus is located at (h, k) and the equation of the directrix is ax+by+c=0. The expression for the square of the distance from (x, y) to the point (h, k) is ...
(d₁)² = (x-h)²+(y-k)²
The expression for the square of the distance from (x, y) to the directrix line is
(d₂)² = (ax+by+c)²/(a²+b²)
Equating these expressions gives the equation of the parabola.
(x-h)²+(y-k)² = (ax+by+c)²/(a²+b²)
When the directrix is parallel with one of the axes, one of the coefficents "a" or "b" is zero and the equation becomes much simpler. Often, it would be easier to make use of the formula (for a directrix parallel to the x-axis):
y = 1/(4p)*(x -h)² +k
where the (h, k) here is the vertex, the point halfway between the focus and directrix, and "p" is the (signed) distance from the focus to the vertex. (p is positive when the focus is above or to the right of the vertex.)
